Effects of Surface Turbulence Flux Parameterizations on the MJO: The Role of Ocean Surface Waves

Olawale James Ikuyajolu aEarth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia
bProgram in Ocean Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia
cFluid Dynamics and Solid Mechanics (T-3), Los Alamos National Laboratory, Los Alamos, New Mexico

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Luke Van Roekel cFluid Dynamics and Solid Mechanics (T-3), Los Alamos National Laboratory, Los Alamos, New Mexico

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Steven R. Brus dMathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois

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Erin E. Thomas cFluid Dynamics and Solid Mechanics (T-3), Los Alamos National Laboratory, Los Alamos, New Mexico

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Yi Deng bProgram in Ocean Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia

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James J. Benedict cFluid Dynamics and Solid Mechanics (T-3), Los Alamos National Laboratory, Los Alamos, New Mexico

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Abstract

This study investigates the sensitivity of the Madden–Julian oscillation (MJO) to changes to the bulk flux parameterization and the role of ocean surface waves in air–sea coupling using a fully coupled ocean–atmosphere–wave model. The atmospheric and ocean model components of the Energy Exascale Earth System Model (E3SM) are coupled to a spectral wave model, WAVEWATCH III (WW3). Two experiments with wind speed–dependent bulk algorithms (NCAR and COARE3.0a) and one experiment with wave-state-dependent flux (COR3.0a-WAV) were conducted. We modify COARE3.0a to include surface roughness calculated within WW3 and also account for the buffering effect of waves on the relative difference between air-side and ocean-side momentum flux. Differences in surface fluxes, primarily caused by discrepancies in drag coefficients, result in significant differences in MJO’s properties. While COARE3.0a has better convection–circulation coupling than NCAR, it exhibits anomalous MJO convection east of the date line. The wave-state-dependent flux (COR3.0-WAV) improves the MJO representation over the default COARE3.0 algorithm. Strong easterlies over the Pacific Ocean in COARE3.0a enhance the latent heat flux (LHFLX). This is responsible for the anomalous MJO propagation after the date line. In COR3.0a-WAV, waves reduce the anomalous easterlies, leading to a decrease in LHFLX and MJO dissipation after the date line. These findings highlight the role of surface fluxes in MJO simulation fidelity. Most importantly, we show that the proper treatment of wave-induced effects in bulk flux parameterization improves the simulation of coupled climate variability.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Olawale James Ikuyajolu, olawale@lanl.gov

Abstract

This study investigates the sensitivity of the Madden–Julian oscillation (MJO) to changes to the bulk flux parameterization and the role of ocean surface waves in air–sea coupling using a fully coupled ocean–atmosphere–wave model. The atmospheric and ocean model components of the Energy Exascale Earth System Model (E3SM) are coupled to a spectral wave model, WAVEWATCH III (WW3). Two experiments with wind speed–dependent bulk algorithms (NCAR and COARE3.0a) and one experiment with wave-state-dependent flux (COR3.0a-WAV) were conducted. We modify COARE3.0a to include surface roughness calculated within WW3 and also account for the buffering effect of waves on the relative difference between air-side and ocean-side momentum flux. Differences in surface fluxes, primarily caused by discrepancies in drag coefficients, result in significant differences in MJO’s properties. While COARE3.0a has better convection–circulation coupling than NCAR, it exhibits anomalous MJO convection east of the date line. The wave-state-dependent flux (COR3.0-WAV) improves the MJO representation over the default COARE3.0 algorithm. Strong easterlies over the Pacific Ocean in COARE3.0a enhance the latent heat flux (LHFLX). This is responsible for the anomalous MJO propagation after the date line. In COR3.0a-WAV, waves reduce the anomalous easterlies, leading to a decrease in LHFLX and MJO dissipation after the date line. These findings highlight the role of surface fluxes in MJO simulation fidelity. Most importantly, we show that the proper treatment of wave-induced effects in bulk flux parameterization improves the simulation of coupled climate variability.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Olawale James Ikuyajolu, olawale@lanl.gov

1. Introduction

The Madden–Julian oscillation (MJO) is a dominant mode of intraseasonal variability in the tropics with a period of approximately 30–60 days. The MJO is characterized by an eastward-moving (about 5 m s−1) large-scale envelope of enhanced precipitation in the equatorial regions that propagates from the western Indian Ocean, across the Maritime Continent, and dissipates near the date line in the Pacific Ocean (Madden and Julian 1972; Weickmann et al. 1985). Its amplitude during boreal winter is more pronounced than in boreal summer. The MJO basic features have been extensively documented in several studies (Madden and Julian 1972, 1994; Zhang 2005; Zhang et al. 2020; Jiang et al. 2020).

The MJO plays an important role in the global weather–climate system, as it has a profound effect on patterns of rainfall, temperature, and atmospheric circulation throughout the tropics and beyond (Lawrence and Webster 2002; Pai et al. 2011; Bessafi and Wheeler 2006; L’Heureux and Higgins 2008; Lin et al. 2009; Vitart 2009; Lorenz and Hartmann 2006; Grimm 2019; Taraphdar et al. 2018; Lee and Seo 2019; Zhou et al. 2012). During the active phase, MJO affects numerous weather patterns based on its intensity and location by forcing Rossby wave trains (teleconnection patterns) that propagate out of the tropics into the extratropics (Hoskins and Karoly 1981; Sardeshmukh and Hoskins 1988). Consequently, MJO provides a source of predictability for seasonal to subseasonal forecasting systems (Waliser et al. 2003; Pegion and Sardeshmukh 2011; Zhang et al. 2013). Despite the importance of MJO signals in seasonal and subseasonal forecasts of extreme weather events, climate models still experience difficulties in simulating several MJO properties such as formation, propagation, maintenance, and spatiotemporal teleconnections (Jiang et al. 2020; Zhang et al. 2006; Ahn et al. 2017, 2020; Hung et al. 2013; Jiang et al. 2015). For example, only 25% of the 27 models in a recent MJO intercomparison study adequately project the eastward propagation characteristics of MJO (Jiang et al. 2015).

Many studies have demonstrated that air–sea interaction modulates the intraseasonal oscillations (Shinoda et al. 1998; Sobel et al. 2008, 2010; DeMott et al. 2015). On intraseasonal time scales, Woolnough et al. (2000) reported a coherent relationship between MJO convection, surface fluxes, and sea surface temperature (SST). Intraseasonal latent heat flux (LHFLX) anomalies account for roughly 7%–10% of MJO precipitation and play an important role in the column-integrated intraseasonal moist static energy (MSE) budget (Araligidad and Maloney 2008; Bui et al. 2020; Riley Dellaripa and Maloney 2015; DeMott et al. 2016; Maloney 2009; Sobel et al. 2014). Surface latent heat fluxes represent a diabatic energy source that plays a critical role in maintaining MJO through its positive correlation with column moist static energy (Kim et al. 2011; Maloney and Sobel 2004).

In global climate models (GCMs), turbulent air–sea fluxes are parameterized using the aerodynamic bulk formulas (e.g., Large and Pond 1981, 1982; Large and Yeager 2004, 2009; Fairall et al. 2003). Hsu et al. (2022) found that MJO simulation in climate models is sensitive to the choice of the bulk formula used to calculate air–sea fluxes. Different bulk parameterizations are currently used in GCMs, and their discrepancies lie in the calculation of the transfer/drag coefficients (Bonino et al. 2022). As a result, there are differences in the estimation of turbulent air–sea fluxes. While Coupled Model Intercomparison Project (CMIP) models consist of at least 10 different bulk algorithms, the Large and Yeager (2009, hereafter referred to as NCAR) algorithm and Coupled Ocean–Atmosphere Response Experiment version 3.0 algorithm (COARE3.0; Fairall et al. 2003) with their modified versions are widely used. Differences in bulk algorithms lead to global mean changes in the energy and water cycles in forced ocean–sea ice simulations (Reeves Eyre et al. 2021). In an ocean-only experiment, Bonino et al. (2022) found that SST in the COARE3.0a simulation was warmer than in the NCAR due to less evaporation (less LHFLX into the atmosphere). These results suggest that the mean state of GCMs is sensitive to the choice of surface flux algorithm. As MJO is also sensitive to the background state (Inness and Slingo 2003; Gonzalez and Jiang 2017; Kang et al. 2021), it is important to investigate the sensitivity of MJO to the choice of surface turbulent flux parameterization.

Neutral transfer/drag coefficients, which depend on sea-state roughness driven by ocean surface gravity waves, are typically parameterized based on statistical analysis of surface wind speed derived from ship and buoy measurements over short spatial and temporal scales (Large and Pond 1981, 1982; Fairall et al. 1996, 2003). Ocean surface gravity waves, driven by energy and momentum from steady winds blowing over the ocean surface, influence numerous physical processes at the air–sea interface, including momentum and energy fluxes, gas fluxes, upper-ocean mixing, sea spray production, ice fracture, coastal inundation, and surface albedo (Cavaleri et al. 2012). However, ocean waves are poorly represented or often neglected in Earth system models (ESMs) due to their small spatiotemporal scales and high computational cost. Recent studies on the inclusion of wave-induced effects in surface flux algorithms have found significant global and regional climate impacts (Law Chune and Aouf 2018; Song et al. 2012; Shimura et al. 2017; Qiao et al. 2013; Fan and Griffies 2014; Li et al. 2016). For example, Shimura et al. (2017) showed that enhanced wind speeds due to the inclusion of wave-state-dependent roughness lead to significant changes in tropical precipitation. Substantial interaction exists between the MJO and surface waves in tropical oceans. From the western tropical Indian Ocean to the eastern tropical Pacific, MJO-induced surface zonal winds covary with significant wave height, peak wave period, and zonal wave energy flux (Marshall et al. 2015). Hilmi et al. (2018) also studied the impact of the MJO on wave height and wind speed in Indonesian Seas. According to the study, the MJO exerts the strongest influence in DJF during phase 5, increasing wind speed and significant wave height in the Indonesian Seas by 6 m s−1 and 30 cm, respectively, but decreasing them during DJF and MAM phase 3 and JJA phase 4. Previous studies about how the MJO and waves interact mostly focus on how the MJO affects waves, without considering how waves might also influence the MJO. Even though surface waves have smaller motion scales compared to the MJO, it is important to note that how we represent these small-scale processes can have a substantial impact on how accurately larger-scale processes are simulated in models. Ocean waves play a crucial role in many physical processes at the air–sea interface, and MJO dynamics are particularly sensitive to alterations in surface winds and heat fluxes (Woolnough et al. 2000; Kim et al. 2011; Maloney and Sobel 2004). The integration of ocean waves into the bulk flux parameterization induces modifications to ocean surface roughness/drag coefficients, subsequently leading to changes in surface winds and heat fluxes. The wave-induced changes in surface wind and heat fluxes ultimately affect MJO characteristics.

Given the sensitivity of the mean climate to the choice of surface turbulent flux parameterizations, the significance of ocean surface waves within the air–sea interface together with the growing incorporation of surface wave models as a standard GCM component, and the dominant role of surface fluxes in simulating several MJO properties, the purpose of this study is to investigate the impacts of two widely used surface turbulent flux parameterizations and wave-state-dependent flux on MJO. To this end, we coupled the WAVEWATCH III wave model (Tolman 2002) to the atmospheric and ocean model components of the Energy Exascale Earth System Model (E3SM) version 2 (Golaz et al. 2022).

While we make reference to the observed MJO properties, the validation of the modeled MJO is not the focus of this study. Here, the main objective is to document its mean response to changes in the bulk flux parameterization. The rest of this paper is organized as follows: Section 2 provides an overview of the bulk flux algorithms along with the wave-state-dependent flux; section 3 gives a brief description of the models, experimental design, observational data, and methodology; the results section, section 4, presents the mean state, MJO characteristics, and MSE budget analysis; and section 5 concludes the paper with further discussion and conclusions.

2. Surface turbulent flux parameterizations

This section presents an overview of the two bulk surface flux formulas and wave-state-dependent flux parameterization. The surface wind stress (momentum flux), sensible heat fluxes, and LHFLX provide surface boundary conditions for the lower atmosphere and upper ocean. Using near-surface variables such as SST, wind speed, air temperature, humidity, and empirically determined bulk transfer/drag coefficients, fluxes in most GCMs are computed from aerodynamic bulk formulas as
windstress:τ=ρaCD|U|(UzUo),
sensibleheatflux:QH=ρacpCH|U|(θzθo),
latentheatflux:QE=ρaLυCE|U|(qzqo),
where the transfer coefficients for wind stress, sensible heat, and latent heat are CD, CH, and CE, respectively; qz, Uz, and θz are the specific humidity, 10-m wind speed, and 2-m air temperature, respectively; z is the reference height above the ocean; θo, qo, and Uo are the potential temperature, saturation specific humidity, and current at the ocean surface, respectively; ρa is the air density; cp is the specific heat capacity of moist air; Lυ is the latent heat of vaporization; and |U| is the wind speed relative to the surface ocean current and gustiness (e.g., Jabouille et al. 1996) if present. Unlike other bulk variables that are measurable quantities, drag coefficients are approximated. The uncertainty in drag coefficients is a leading source of differences between existing bulk flux algorithms (Bonino et al. 2022). However, there are also slight differences in |U|, Lυ, qz, and θo that can also lead to differences in surface fluxes. The drag coefficients, CD, CE, and CH, are parameterized as functions of the stability of the atmospheric surface layer and roughness lengths [Eq. (A1)], and algorithms parameterize them in different ways. When the stability correction (ψm,e,h) approaches zero, CD becomes the neutral drag coefficient CDN, which only depends on the roughness length. The roughness length is also often parameterized as a function of wind speed.

In this study, we focus on two of the most widely used bulk algorithms: the NCAR algorithm (Large and Yeager 2009) and the COARE3.0 algorithm (Fairall et al. 2003). For a more theoretical background on these bulk algorithms, see Brodeau et al. (2017) and Bonino et al. (2020).

a. Traditional bulk formulas: Wind speed–dependent transfer coefficients

According to Bonino et al. (2022), the major discrepancies in bulk algorithms caused by CD are primarily due to the neutral drag coefficients and not the stability correction. Hence, we focus on CDN.

Based on field experiments (Large and Pond 1981, 1982; Large and Yeager 2009), the NCAR algorithm parameterizes the neutral drag coefficient for momentum as a function of neutral wind speed only at 10 m (U10N):
CDN=(0.0027U10N1+0.000142+0.0.0000764U10N).
This implies that CD is a function of wind speed. Equation (2) systematically omits the computation of CDN via roughness length zo and consequently of zo using the Charnock parameter α. The α, a dimensionless parameter, accounts for increased aerodynamic roughness as wave heights grow due to increasing surface stress. The moisture CH and heat CE transfer coefficients are functions of CD [Eqs. (20b) and (20c) of Bonino et al. 2020].
Unlike NCAR, the COARE3.0a parameterizes CDN as a function of the momentum roughness length zo, then zo as a function of α, and finally α as a function of U10N:
CDN=κ2[ln(10zo)]2,
zo,m=0.11νu*+αu*2g,α={0.011,|U|<10ms10.011+0.0078(|U|10),10ms1<|U|<18ms10.018,|U|>18ms1,
where u* is the scaling parameter for wind or friction, g is the gravitational acceleration constant, κ is the von Kármán constant, and ν is the kinematic viscosity of dry air. Therefore, by combining Eqs. (3) and (4), the momentum drag coefficient has embedded functions: CD{zo,m[α(u)]}. Sensible heat (zo,h) and latent heat (zo,e) roughness lengths are functions of zo,m [Eq. (18) of Bonino et al. 2020]; thus, CE, and CH are indirect functions of CD.

Figure 1 shows the neutral drag coefficients (CDN and CEN) as a function of U10N for both algorithms. Under light wind conditions (u < 5 m s−1), NCAR CDN estimates higher momentum than COARE3.0a, whereas under above light wind conditions (u > 5 m s−1), NCAR CDN estimates lower momentum than COARE3.0a. This regime shift is also shown in Fig. 2a of Bonino et al. (2020) which shows the Charnock parameter–U10N relationship. Unlike CDN, NCAR’s CEN is greater than that of COARE3.0a under all conditions (Fig. 1).

Fig. 1.
Fig. 1.

Neutral drag coefficient CDN and moisture transfer coefficient CEN, represented by thick and dashed lines, respectively, plotted as functions of the neutral wind speed at 10 m (U10N) for NCAR (in blue) and COARE (in red). This figure is adapted from Bonino et al. (2020) and Brodeau et al. (2017).

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

b. Wave-state-dependent bulk formula

Ocean surface waves influence the momentum flux in two ways. First, the modification of surface roughness acts on the air side of the momentum flux, which subsequently influences the heat fluxes. Second, a wave that is growing (or dissipating) reduces (or increases) the total momentum flux transferred from the atmosphere into the ocean, resulting in a different momentum flux on the ocean side.

1) Air-side momentum flux

The neutral drag coefficient (or Charnock parameter α) is a function of wave state but has traditionally been parameterized as a function of wind speed. Due to the remote generation of swell waves, sea surface roughness or wave state can vary at a given local wind speed. Unlike wind-sea waves which are waves generated by local winds, swells are remotely generated by storms, travel great distances, and are generally decoupled with the local wind. The oversimplification of sea surface roughness is therefore likely to contribute to systematic errors in the estimation of surface fluxes. Moreover, under open ocean conditions, mixed sea states (wind sea and one or more swells) frequently occur and cannot be fully described by local winds. To evaluate the drag coefficient under mixed sea state conditions, Janssen (1991) developed a Charnock parameter [αw: Eq. (5)], which depends on the wave-induced stress τwavatm and the total stress τatm(wave). These stresses are calculated from a third-generation spectral wave model that describes the frequency–direction spectra of waves. This is the α formulation adopted in our coupled framework.
αw=αo1τwavatmτatm(wave);αo=0.01.
Most of the details of Eq. (5) are presented here, while the rest can be found in the appendix. The τwavatm [Eq. (A2)] is the wave-supported stress: input stress from the atmosphere to the wave (for growing), and τatm(wave) is the total stress computed by the wave model without stability correction [ψm,e,h = 0 in Eq. (A1)]. Since the sensible and latent heat roughness lengths are a function of zo,m, CE and CH also indirectly include the wave-state modification via αw.

2) Ocean-side momentum flux

In traditional bulk algorithms, the air-side τatm momentum flux is assumed to be identical to the ocean-side τocn momentum flux (τocn = τatm). However, this is only valid when waves and winds are in equilibrium resulting in continuity of momentum (fluxes) at the air–sea interface (Pierson and Moskowitz 1964). Ocean waves are often not in equilibrium with the local winds (Hanley et al. 2010), and growing and decaying waves affect the sea state. As waves grow or decay, the stress on the ocean side decreases or increases, respectively, relative to the airside stress. Previous studies have found that the absolute relative difference between τocn and τatm is up to 10% (Donelan 1998; Ardhuin et al. 2004; Wu et al. 2019, 2022) and up to 30% (Alari et al. 2016) in extreme cases. Such complex processes can only be adequately represented by a spectral wave model. Thus, considering the buffer role of surface waves at the air–sea interface, the total balance on the ocean-side momentum thus becomes
τocn=τatmτwav;τwav=τwavatmτocnwav,
τocn=τatm(τwavatmτocnwav).
The τwav is the total wave stress; τwavatm is the wave-supported stress: input stress from the atmosphere to the wave (for growing); and τocnwav is the dissipation stress from the wave to the ocean (always negative). The remaining details are given in the appendix. The τwavatmandτocnwav [Eqs. (A2) and (A3)] are calculated from a 2D wave spectral model. Only when the momentum input by the wind τwavatm is balanced by the momentum released through wave breaking τocnwav, resulting in a fully developed sea, will the stress on the ocean side τocn balance the atmospheric stress τatm.
The previous formulation of the ocean-side momentum assumed that the wave effects only act on the norm of τatm and not on its orientation (Alari et al. 2016; Law Chune and Aouf 2018; Wu et al. 2019). Instead of using Eq. (6a) directly, the atmospheric wind stress τatm was corrected as follows:
τocn=τ˜τatm;τ˜=τocn(wave)τatm(wave),
where τ˜ is the normalized momentum flux and τocn(wave) and τatm(wave) are the atmospheric and ocean wind stress computed within the wave model without stability correction. Equation (7) does not take into account the slight change in τocn direction induced by the waves. However, the directional difference between τocn and τatm exceeds 3.5°, in the mid- and high latitudes 10% of the time (Wu et al. 2022).

To account for both the magnitude and directional differences between τocn and τatm, this study utilizes the momentum balance defined by Eq. (6a) directly. More details can be found in the coupling strategy section.

3. Model description, experimental design, data, and methodology

a. Models

To account for wave-state-dependent air–sea fluxes [Eq. (6)], we communicate part of the WAVEWATCH III (WW3) state via the coupler to the atmospheric and ocean model components of E3SM. The following lists provide a brief description of each model and the coupling strategy for E3SM and WW3:

  • WW3: This is a third-generation spectral wave model developed at the U.S. National Centers for Environmental Prediction (NOAA/NCEP) (Komen et al. 1994) from the wave model (WAM) (The Wamdi Group 1988). It has been used widely to simulate ocean waves in many oceanic regions for various science and engineering applications (Chawla et al. 2013; Alves et al. 2014; Cornett 2008; Wang and Oey 2008). For large-scale applications, the evolution of the wave action density in WW3 is expressed in spherical coordinates as shown in Eq. (A4). The E3SM version 2 standard (low) resolution model is coupled with WW3 (v6.07), which is configured with a spectral resolution of 36 directions and 50 frequency bands and an unstructured mesh of 225 km that matches the ocean mesh (∼30 km) of E3SMv2 at the coast.

  • E3SM: We used the E3SM version 2 standard (low) resolution (Golaz et al. 2022). The E3SM is the U.S. Department of Energy’s (DOE) Earth system model for addressing DOE mission questions, including interests related to water availability, coastal processes and hazards, and biogeochemistry. The components include the atmosphere [E3SM atmosphere model (EAMv2)], ocean [Model for Prediction Across Scales-Ocean (MPAS-Ocean)], land [E3SM Land Model version 2 (ELMv2)], sea ice (MPAS-Seaice), and river routing [Model for Scale Adaptive River Transport (MOSARTv2)] models. Approximate model component horizontal grid cell resolutions are 100 km for EAM and ELM, 30–60 km for MPAS-Ocean and MPAS-Seaice, and 55 km for MOSART. See Golaz et al. (2022) for further description. Currently, E3SM has three options for bulk formula, namely, the NCAR, COARE3.0a, and University of Arizona (UA) algorithms (Zeng et al. 1998).

  • E3SM–WW3 coupling strategy: We describe only the fields relevant to the current study, particularly related to the computation of αw in Eq. (5), as well as τwavatm and τocnwav in Eq. (6). In our coupling framework, we adopted the αw formulation based on directional wave spectra [Eq. (5)] for computation of transfer coefficients and modified the ocean-side stress τocn using Eq. (6). The meridional and zonal winds are passed from EAM to WW3 via the coupler. WW3 then internally computes τatm(wave) and subsequently αw, τwavatm, and τocnwav. WW3 passes αw to the coupler for bulk algorithm calculations. Also, τwavatm and τocnwav are passed from WW3 to MPAS-Ocean for wave modification of the ocean-side momentum flux [Eq. (6a)]. This coupling strategy used two different bulk algorithms, with and without stability correction [ψm,e,h; Eq. (A1)], to compute τatm in Eq. (6a) and τatm(wave) in Eq. (5). Although the computation of bulk algorithms is inconsistent, it does not violate momentum conservation [Eq. (6a)]. We assume a momentum balance among the three systems: atmosphere (atm), ocean (ocn), and waves (wav). The trapped or dissipated stress, controlled by τwav, subsequently modifies the momentum flux transferred from the atmosphere τatm to the ocean τocn. Therefore, waves only redistribute momentum flux at any given time.

b. Experiment design

The experiments used in this study are listed in Table 1 along with how neutral drag and ocean-side wind stress are altered in each case. We conducted three experiments type: Two experiments with traditional (wind speed–dependent) bulk algorithms, NCAR and COARE3.0a (referred to as NCAR and COR3.0a hereafter), and one experiment with a wave-state-dependent flux (COR3.0a-WAV hereafter). The NCAR bulk formula is the default flux parameterization in E3SM, and it is currently impractical to include wave-dependent momentum flux into the NCAR formula due to the absence of the Charnock parameter α in its algorithm (section 2a). Since COARE3.0a parameterizes the drag coefficient as a function of α, the wave state modification is implemented in this algorithm.

Table 1.

Summary of the experimental setup showing the modifications to momentum drag coefficient parameterization and wind stress at the air–sea interface. The underlined variables are from the spectral WAM. Here, we only show CDN modifications since it is the fundamental difference among algorithms used in this study. The modifications of CD, CE, and CH follow as explained in section 2.

Table 1.

The experiments use the CMIP6 preindustrial control forcing. The control experiment, NCAR, is run for 400 years. The COR3.0a and COR3.0a-WAV experiments branch from the control at year 300 and are run for 100 years. We analyzed the last 30 years of each simulation.

c. Observational data

We use a few observational datasets to compare our results, but we focus primarily on documenting mean responses of MJO to bulk flux algorithms. We use daily averaged rainfall analyses from the Tropical Rainfall Measuring Mission (TRMM 3B42 version 6; Huffman et al. 2007), outgoing longwave radiation (OLR) from the Advanced Very High Resolution Radiometer (AVHRR; Liebmann and Smith 1996) provided by the NOAA/Earth System Research Laboratory (ESRL), SST from the Hadley Centre Sea Ice and SST (Rayner et al. 2003), and surface LHFLX from the objectively analyzed air–sea fluxes (OAFlux; Yu and Weller 2007). Upper- (250 hPa) and lower-tropospheric (850 hPa) zonal and meridional winds (U250, V250 and U850, V850, hereafter) are obtained from the fifth-generation ECMWF atmospheric reanalysis (ERA5; Hersbach et al. 2020). For the MSE budget analysis, we used ERA5 4-D specific humidity, air temperature, tropospheric zonal and meridional winds, geopotential height, pressure velocity, and surface and radiative fluxes at the lower and upper boundaries of the atmosphere. While TRMM rainfall data are for the period of 1998–2010, other aforementioned datasets cover the period 1981–2010.

d. Methodology

This study focuses on the extended boreal winter season, November–April, when the MJO amplitude is more pronounced. All datasets are interpolated onto a 1° × 1° horizontal grid. Intraseasonal anomalies of each variable are obtained by removing the mean annual cycle and then filtered by applying a 20–100-day Lanczos bandpass filter. The MJO diagnostics are based on the CLIVAR MJO Working Group diagnostics package (Waliser et al. 2009). To understand the moistening processes associated with the maintenance and propagation of the MJO, we diagnose the intraseasonal vertically integrated (100–1000 hPa) MSE budget based on the following equation:
mt=Vhmwmp+LHFL X+SHFL X+LW+SW+residm,
where m = CpT + gz + Lυq denotes MSE, V = ui + υj is the tropospheric wind vector, h=(i/x)+(j/y) is the horizontal gradient, T is the air temperature, q is the specific humidity, z is the geopotential height, Cp is the specific heat of dry air at constant pressure, g is the gravitational acceleration constant, LHFLX is the latent heat flux, SHFLX is the sensible heat flux, LW is the longwave radiative heating rate, SW is the shortwave radiative heating rate, and residm is the budget residual, which is obtained by subtracting all RHS terms from MSE tendency (m/t). The prime (′) denotes intraseasonal anomaly, and the angle brackets (〈〉) indicate the mass-weighted vertical integral from 1000 to 100 hPa.

4. Results

a. Mean state

Previous studies have shown that mean state biases such as those related to the mean westerly wind (Inness and Slingo 2003), the horizontal gradient of mean moisture around the Maritime Continent and equator (Kim et al. 2014; Gonzalez and Jiang 2017; DeMott et al. 2019; Ahn et al. 2020), and gross moist stability (Benedict et al. 2014) most likely lead to the poor simulation of MJO in GCMs. In light of this, we first evaluate the response of the mean state to the choice of surface turbulent flux parameterizations. Since SHFLX is an order of magnitude smaller than LHFLX in tropical ocean regions, we exclude the examination of SHFLX in our study. Given that MJO propagation is known to be sensitive to the background moisture distributions (Gonzalez and Jiang 2017), we also assess the impact of the choice of surface turbulent flux parameterizations on the horizontal distribution of column-integrated water vapor.

1) Wind stress

Figure 2 illustrates the simulated mean state of turbulent fluxes and SST for each experiment and observation, along with their respective differences in the extended boreal winter season. Over most of the tropical ocean, the observed wind stress (Fig. 2a-1) is predominantly easterly (blue shades), whereas it is westerly (yellow shades) south of the Maritime Continent. Figure 2 (black contour lines) shows that all model experiments tend to produce more westerly wind stress (blue shades are less blue or even shift to yellow, and yellow shades intensify) across most of the tropics and subtropics. Importantly, the simulated wind stress immediately south of the equator in the Indian Ocean is easterly (blue shades), while the observed wind stress in the region is westerly (yellow shades). This is consistent with the wind stress bias among CMIP5 models (Simpson et al. 2018). Recall that the drag coefficient CD is not a measurable quantity. So even with satellite-based surface winds, observation-based products still depend on similar bulk algorithms as GCMs. In fact, Risien and Chelton (2008) showed that different bulk algorithms produce different stress estimates for the Quick Scatterometer (QuikSCAT). Consequently, it is unclear whether observations overestimate or GCMs underestimate easterly wind stress (Simpson et al. 2018).

Fig. 2.
Fig. 2.

November–April (left) mean zonal wind stress (vectors; N m−2), (middle) LHFLX (W m−2), and (right) SST (°C) for (a-1),(b-1), (c-1) observations, (a-2),(b-2),(c-2) NCAR, (a-3), (b-3),(c-3) COR3.0a, and (a-4),(b-4),(c-4) COR3.0a-WAV. The contours (black line) depict the difference between each experiment and observation. The pattern correlation and RMSE against the observations are labeled at the top of each panel. (a-5),(b-5),(c-5) The difference between the COR3.0a and NCAR, and (a-6),(b-6),(c-6) the difference between the COR3.0a-WAV and COR3.0a. The regions exceeding the 95% confidence level are stippled.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Over the Bay of Bengal extending into the northern part of the central tropical Pacific Ocean and the south Indian Ocean, COR3.0a simulates stronger easterlies than NCAR (Fig. 2a-5). In these regions, |U| > 6 m s−1, indicating that CDNNCAR<CDNCOR3.0a (Fig. 1). As a result, in the absence of ocean–atmosphere feedback, COR3.0a should estimate stronger wind stress. Similarly, along the southern equatorial Indian Ocean and northeast coast of Australia where u < 6 m s−1 with CDNNCAR>CDNCOR3.0a, COR3.0a estimates weaker wind stress. However, both algorithmic differences and ocean–atmosphere feedbacks dominate wind stress changes globally.

While the effects of waves on the air-side wind stress (τatm) depend on the Charnock parameter [αw; Eq. (5)], the ocean wind stress depends on αw and the total wave stress τwav. The COR3.0a-WAV simulated higher values of αw than COR3.0a α formulation [Eq. (4)]. Based on the bulk algorithm and without considering feedbacks, an increase in the Charnock parameter α results in higher wind stress. However, when feedbacks are taken into account, an increase in the drag coefficient leads to a reduction in the surface wind, which ultimately circles back to decrease the wind stress. Thus, in this case, waves are sink of momentum. This pattern is observed in most regions when comparing the annual mean difference in wind stress between the COR3.0a-WAV and COR3.0a experiments. However, during the boreal winter, surface ocean waves notably induce westerly wind stress near 30°N, the boundary between easterly and westerly wind stress regions (Fig. 2a-6). When comparing Figs. 2a-5 and 2a-6, it becomes apparent that waves mitigate some of the wind stress differences between COR3.0a and NCAR in most regions.

2) Latent heat

GCMs often overestimate LHFLX in tropical regions (Brunke et al. 2003; Cao et al. 2015; Zhang et al. 2018). Our results (Figs. 2b-1b-4) also demonstrate that E3SM overestimates LHFLX during the boreal winter, especially over the western tropical Pacific Ocean, regardless of the bulk algorithm used. However, all experiments adequately represent the observed spatial pattern as indicated by the spatial correlation (top of each panel). While Cao et al. (2015) suggests that the positive bias originates from the wind speed bias, Zhou et al. (2020) discovered that near-surface humidity plays a more significant role in contributing to the bias than wind speed in Atmospheric Model Intercomparison Project (AMIP) models. However, given Zhou et al. (2020) analyzed atmosphere-only simulations, the wind speed bias is likely underestimated.

Figure 2b-5 shows the difference between NCAR- and COR3.0a-simulated LHFLX. In some areas, such as the northwest Pacific Ocean and the Arabian Sea, COR3.0a exhibits less evaporation, while in others, such as the northeast Pacific Ocean, Bay of Bengal, and southeast tropical Indian Ocean, it exhibits more evaporation. Under all conditions, the moisture transfer coefficient for NCAR is greater than COR3.0a (CENCAR>CECOR3.0a). Therefore, it is expected that COR3.0a should simulate less evaporation, a finding that is also supported by Bonino et al. (2022) in an ocean-only experiment. The spatial patterns in Fig. 2b-5 do not provide a clear distinction between the algorithms due to ocean–atmosphere feedbacks; however, COR3.0a has less evaporation than NCAR in general. The enhanced evaporation simulated by COR3.0a relative to NCAR in some regions during boreal winter is likely wind-driven. Surface wind changes, caused by wind stress modifications, feed back into LHFLX.

Analogous to the impact of waves on wind stress, waves also act to reduce the LHFLX difference between COR3.0a and NCAR in most regions (Fig. 2b-6) during the boreal winter, leading to opposite patterns in Figs. 2b-6 and 2b-5. The wave-induced LHFLX changes are mainly wind-driven, rather than the differences in moisture exchange coefficients. For example, when comparing Figs. 2a-6 and 2b-6, the enhanced (reduced) LHFLX over the northwest (northeast) Pacific Ocean is due to stronger (weaker) westerlies (easterlies). For the annual mean (not shown), waves generally act to enhance evaporation.

3) Sea surface temperature

As shown at the top of Figs. 2c-12c-4, all experiments display a strong spatial correlation of 0.93 when compared with observations. The SST bias in the three experiments also follows a similar spatial pattern (Figs. 2c-22c-4), characterized generally by a cold SST bias in the Northern Hemisphere (NH) and a warm bias in the Southern Hemisphere (SH). This pattern is consistent with the SST bias observed in the E3SM historical (1985–2014) simulation (Golaz et al. 2022).

Figure 2c-5 shows warmer SST in COR3.0a than NCAR during the boreal winter season. Consequently, COR3.0a tends to enhance (reduce) SST bias in the SH (NH). This difference in SST is also evident throughout all seasons (not shown). The increase in SST cannot be solely attributed to the LHFLX pattern difference and is, thus, inconsistent with the findings of the ocean-only simulation by Bonino et al. (2022). Here, in a coupled simulation where surface winds vary, SST changes are also influenced by changes in the upper ocean dynamics such as entrainment, advection, and upwelling that are driven by changes in surface flux parameterization. For example, the pronounced warm blob in the Kuroshio–Oyashio region is due to advection and mixing processes. These modifications of upper ocean dynamics, driven by differences in the wind stress and LHFLX, also result in an increased ocean heat content (OHC) in COR3.0a compared to NCAR. In addition, individual El Niño–Southern Oscillation (ENSO) events in COR3.0a are of higher magnitude compared to NCAR due to increased OHC in COR3.0a (not shown).

In Fig. 2c-6, waves induce an El Niño–like pattern over the tropical Pacific Ocean with colder SST in the Kuroshio. In the Indian Ocean, wave effects lead to an increase in SST near the coast of Somalia, the Arabian Sea, and the southern Indian Ocean. Again, as with the NCAR and COR3.0a SST differences, the LHFLX wave-induced pattern (Fig. 2b-5) cannot explain the SST response in some regions. While LHFLX predominantly controls SST changes over the northeast Pacific Ocean, modifications in upper ocean dynamics due to changes in wind stress are responsible for SST changes in some regions, e.g., the warm SST over the South Pacific Ocean. A detailed examination of these mean state differences is beyond the scope of this study.

4) Column-integrated water vapor

Figure 3 shows the November–April mean column-integrated water vapor for observations and all experiments. The horizontal distribution of integrated water vapor (IWV) in all experiments aligns closely with observations, and the bias pattern is consistent across all experiments (Figs. 3a-1a-4). Except for the northern part of the equatorial Pacific, COR3.0a generally shows higher IWV than NCAR (Fig. 3a-5), primarily due to the low-level moisture (Fig. S1 in the online supplemental material). This difference could be attributed to the higher SST in COR3.0a compared to NCAR; however, a more in-depth moisture budget analysis is needed for further investigation. In comparison with observations, NCAR exhibits stronger IWV biases than COR3.0a across most of the basins. Waves in COR3.0a-WAV (Fig. 3a-6) modestly reduce the IWV positive biases over the equatorial central and eastern Pacific Ocean, particularly around the date line. There is a slight enhancement of IWV biases in certain regions, such as the western coast of Mexico. Despite this, with the lowest RMSE of 3.41, waves in COR3.0a-WAV generally contribute to a reduction in IWV biases across the basins.

Fig. 3.
Fig. 3.

November–April mean column-integrated water vapor for (a-1) observation and (a-2)–(a-4) difference between each experiment and observation. The pattern correlation and RMSE against the observations are labeled at the top of each panel. (a-5) The difference between the COR3.0a and NCAR, and (a-6) the difference between the COR3.0a-WAV and COR3.0a. The regions exceeding the 95% confidence level are stippled.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Mean state background changes, such as those observed in IWV, strongly suggest that modifications to the bulk flux parameterization can influence MJO representation. Specifically, two notable effects are observed: 1) the enhancement of midlevel moisture with COR3.0a and COR3.0a-WAV (Fig. S1) and 2) the increase in precipitable water near the equator in the Pacific basin in COR3.0a-WAV. These changes may aid MJO propagation by creating a more conducive environment for deep convection and by sharpening horizontal moisture gradients, thereby supporting increased moisture advection crucial for MJO propagation.

b. MJO characteristics

In this section, we evaluate how the aforementioned changes in the mean state due to different bulk algorithms affect the MJO. Analysis methods are employed from both level-1 and level-2 CLIVAR MJO simulation diagnostics (Waliser et al. 2009) to assess the realism of spatial and temporal scales and propagation characteristics of MJO. These metrics include 1) intraseasonal variability (ISV) spatial characteristics, 2) wavenumber–frequency power spectra, 3) eastward and northward propagations, 4) cross spectra of U850 and OLR, and 5) MJO composite life cycle.

1) Intraseasonal variability (ISV)

Figure 4 shows the 20–100-day filtered variance of U850 and OLR, a measure of intraseasonal variability, during the extended boreal winter (November–April). The observed U850 (Fig. 4a-1) shows strong ISV in the southern Maritime Continent (MC), extending into the southern Indian and the central tropical Pacific Oceans. The spatial correlation of 0.9 with observations, as shown at the top of Figs. 4a-24a-4, shows that all experiments capture the fundamental spatial pattern of ISV. Compared with observations, all experiments (Figs. 4a-2a-4) exhibit a strong, positive U850 variance bias in the southern MC and the equatorial western to central tropical pacific.

Fig. 4.
Fig. 4.

ISVs of (left) U850(m2 s−2) and (right) OLR (W2 m−4) during the boreal winter from (a-1),(b-1) observations and (a-2)–(a-4),(b-2)–(b-4) differences between experiments and observations. The pattern correlation and RMSE against the observations are labeled at the top of each panel. (a-5),(b-5) The difference between the COR3.0a and NCAR, and (a-6),(b-6) the difference between the COR3.0a-WAV and COR3.0a.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

In the southern MC, COR3.0a exhibits a U850 ISV that is approximately 20%–25% higher than NCAR (Fig. 4a-5), while north of this region, it is also 20%–25% lower than NCAR. In COR3.0a-WAV, waves (Fig. 4a-6) decrease U850 ISV across most of the region compared to COR3.0a, thereby reducing the strong positive bias in these regions. However, at the Bay of Bengal, waves increase the bias by simulating 15%–20% higher U850 ISV. The root-mean-square error (RMSE) can be used to indicate how well each surface flux parameterization simulates the observed pattern. While the NCAR has an RMSE of 2.78, incorporating wave effects into the COR3.0a simulation reduces the RMSE from 3.03 to 2.58.

The location and pattern of the observed OLR ISV (Fig. 4b-1) are quite similar to that of U850, except that the strong OLR ISV in the Indian Ocean is more locally concentrated to the eastern part and spans across the equator. All experiments exhibit a strong positive bias in the western Indian Ocean, MC, and the equatorial western tropical Pacific extending up the western coast of Mexico (Figs. 4b-2b-4), consistent with Fig. 3 of Kim et al. (2009). While the difference between COR3.0a and NCAR is not uniform (Fig. 4b-5), the positive bias in the equatorial western tropical Pacific Ocean extending up the western coast of Mexico in COR3.0a is smaller than NCAR. In general, including waves (Fig. 4b-6) reduces the positive bias in OLR ISV, especially over the MC. All experiments have similar spatial correlations, with NCAR having the lowest correlation of 0.84. However, NCAR also has the lowest RMSE. The results of the unfiltered mean variance of OLR and U850 follow the same patterns of bias and differences between experiments that are discussed above for the ISV.

2) Wavenumber–frequency power spectra

To isolate MJO’s intraseasonal features in both space and time, we apply wavenumber–frequency power spectra following the Wheeler and Kiladis (1999) method to the U850 and OLR anomalies during the boreal winter (Fig. 5). The power spectra are computed for each year and subsequently averaged over all years of data. We employ the eastward/westward power spectrum ratio (E/W ratio: Zhang and Hendon 1997; Kim et al. 2009) and the ratio of simulated to observed eastward power (E/O ratio: Ahn et al. 2017) metrics within the intraseasonal band (wavenumbers 1–3 and the 30–90-day period) to evaluate the fidelity of eastward propagation. The E/W > 1 indicates that eastward propagation is more dominant within the 30–90-day periods range and E/O values closest to 1 imply eastward power similar to observations.

Fig. 5.
Fig. 5.

Wavenumber–frequency spectra of (a)–(d) U850 and (e)–(h) OLR anomaly of observation and experiments averaged over 10°N–10°S. The ratio of eastward spectral power to westward spectral power (E/W) and the ratio of simulated to observed eastward spectral power (E/O) in the MJO band are labeled at the right above each panel.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

In observations, the dominant spatial scale for U850 is zonal wavenumber 1 (Fig. 5a), while for OLR, it is zonal wavenumbers 1–3 (Fig. 5e) within the 30–90-day periods. The patterns of spectra for all experiments are different from observations. In all experiments (Figs. 5a–d), the U850 anomaly is overestimated and also exhibits a second maximum at a higher frequency (<30-day period) at wavenumber 1. Among experiments, NCAR (Fig. 5b) has the lowest eastward power maxima, whereas waves (Fig. 5d) act to reduce eastward power maxima bias and cause a slight shift to higher frequencies than in COR3.0a (Fig. 5c).

All experiments show eastward-propagating power for OLR in the same frequency range for wavenumbers as in observations (Figs. 5e–h). However, the peak of the eastward power is concentrated at low frequencies (period > 100 days), and a larger westward power than observed occurs at wavenumbers 2 and 3 (to the left of zero frequency). Similar to U850, NCAR (Fig. 5f) has the lowest eastward power maximum. Wave effects (Fig. 5h) decrease the eastward power peak bias and induce a second spectral peak within the 30–90-day periods’ range which is not seen in COR3.0a (Fig. 5g). This second spectral peak in COR3.0a-WAV falls within the period range of observed peak spectra. Similar to the wave impacts on mean states, wave effects also act to shift U850 and OLR spectra in COR3.0a closer to NCAR.

The observed E/W ratio is 2.14 and 2.79 for OLR and U850, respectively. All experiments underestimate (overestimate) E/W ratios in OLR (U850). For OLR, NCAR has the lowest E/W ratio and E/O ratio, indicating a significant eastward propagating bias, yet its eastward power is closest to the observed values. While the E/W ratio in COR3.0a increases from 1.90 to 2.00 in COR3.0a-WAV, getting closer to the observed value, COR3.0a-WAV has a higher E/O ratio. This implies that waves decrease the eastward propagating bias by increasing the magnitude of eastward power and decreasing westward power in COR3.0a. For U850, among the experiments, NCAR exhibits the lowest E/W and E/O ratios of 2.86 and 1.46, respectively, thus simulating eastward and westward power closest to observations. In COR3.0a-WAV, the E/W and E/O ratios are reduced relative to COR3.0a, thereby reducing the strong eastward propagation bias.

Figure 6 illustrates all season zonal wavenumber–frequency spectra of the 10°N–10°S equatorially symmetric component of tropical precipitation divided by the smoothed background spectrum using the Wheeler–Kiladis method (Wheeler and Kiladis 1999). To investigate the details in the MJO band, an enlarged view of the symmetric component is provided. It is evident from Figs. 6a–e, which highlight the differences between observations and COR3.0a, that all experiments generally underestimate tropical precipitation variability associated with Kelvin waves (wavenumbers 2–10 within 3–16-day periods) and MJO-related waves (wavenumbers 1–3 within 30–90-day periods). This result is consistent with previous MJO results in E3SM (Fig. 17 of Golaz et al. 2022). Compared to NCAR, COR3.0a exhibits greater power values at wavenumber 1 and reduced values at wavenumbers 2–3 within the MJO spectral region. However, the differences in the Kelvin spectral region appear to be nonuniform. When comparing COR3.0a and COR3.0a-WAV, the inclusion of waves amplifies the power values bias at wavenumber 1 and diminishes it at wavenumbers 2–3 in COR3.0a (Fig. 6g).

Fig. 6.
Fig. 6.

Wavenumber–frequency power spectra of equatorially symmetric precipitation for (a) observations (TRMM: 1998–2010), (b)–(d) experiments, (e) percentage difference between observations and COR3.0a, (f) percentage difference between NCAR and COR3.0a, and (g) percentage difference between COR3.0 and COR3.0a-WAV. Plotted values represent the summed power from 10°N to 10°S divided by the smoothed background power (the “normalized” power). Solid black lines in each panel represent shallow water dispersion curves for equivalent depths of 12, 25, and 50 m. Key wave types are labeled: Kelvin, equatorial Rossby (n = 1 ER), and MJO.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

As expected, the metrics E/O and E/W (shown at the upper right of Figs. 6a–d) for tropical precipitation follow the pattern of OLR’s metrics among experiments, as previously discussed. COR3.0a-WAV has an E/W ratio of 2.04, which is closest to the observed value of 2.03, while NCAR exhibits an E/O ratio that is the closest to 1 among the experiments. Nonetheless, all experiments demonstrate eastward power that is relatively comparable to the observed values. Waves act to improve eastward propagation in COR3.0a by increasing the magnitude of eastward power and decreasing westward power in COR3.0a. Our results are consistent with the findings of Hsu et al. (2022), who found an increase in the E/W ratio when the NCAR (default) bulk algorithm in E3SM and CESM2 was replaced with the COR3.0a algorithm.

The analysis of wavenumber–frequency spectra for U850, OLR, and precipitation reveals that frequencies characteristics of MJO are sensitive to the choice of surface turbulent flux parameterization. Furthermore, incorporating waves into the COR3.0a bulk algorithm modestly improves the eastward dominant power of convection and circulation.

3) Cross-spectra of U850 and OLR

The circulation anomaly and convection associated with MJO are closely coupled. Consequently, rather than using single variable spectral calculations in wavenumber–frequency space, as shown in Figs. 5 and 6, we employ the cross-spectral method to assess the coherence and phase relationships between convection (OLR) and 850-hPa zonal (U850) winds (Hendon and Wheeler 2008). Figure 7 shows the coherence squared (in colors) and phase (vectors) between equatorial (15°N–15°S) U850 and OLR for both symmetric and antisymmetric components during the boreal winter season. To highlight the salient features within the MJO band, enlarged views of both the symmetric and antisymmetric components are presented. In Fig. 7, vectors represent the phase by which U850 anomalies lag behind OLR anomalies, with an increase in the clockwise direction.

Fig. 7.
Fig. 7.

(left),(middle) The symmetric component (zoom-in details in the MJO band) and (right) asymmetric component (zoom-in the MJO band) of the coherence squared (colors) and phase lag (vectors) between U850 and OLR averaged over 10°N–10°S for (a)–(c) observations and (d)–(l) experiments. Cross-spectra are calculated using daily data during November–April on 256-day-long segments, with consecutive segments overlapping by 206 days. The 0° phase is represented by a vector directed upward and increasing in the clockwise direction. Solid black lines in each panel represent shallow water dispersion curves as in Fig. 6.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Observations (Fig. 7a) exhibit a high degree of coherence and an approximately 90° phase lag between OLR and U850 for zonal wavenumbers 1–3 in the 30–90-day periods’ band. Climate models face challenges in simulating this feature (Waliser et al. 2009), which is also evident in the single variable spectral calculations (Figs. 5 and 6). All experiments exhibit a significant but mostly lower coherency in the MJO band of the symmetric part (Figs. 7e,h,k), along with a phase lag that is similar to the observed value (Fig. 7b). At wavenumber 1, the observed coherency peak spans 35–80-day periods, while the coherency peaks in experiments extend into higher frequencies near 25-day periods.

Since the signal at wavenumber 1 and 30–90-day periods in the symmetric component could be a linear convectively coupled Kelvin wave (Hendon and Wheeler 2008), the experiments may exhibit more linear convectively coupled Kelvin wave activity than observations (Roundy 2008). Due to the symmetric intrinsic property of equatorial Kelvin waves, the antisymmetric part (Figs. 7c,f,i,l) is employed to distinguish the MJO signal from high-frequency convectively coupled Kelvin waves. In the antisymmetric component, both observations and experiments exhibit significant coherency at wavenumber 1, with observations showing higher coherency (0.25–0.40) compared to experiments (0.15–0.35). In the asymmetric part, all experiments show significant coherency (0.15–0.30) for wavenumber 1 within 30–90-day periods, which is slightly weaker than the observed coherency (0.25–0.40).

Within the MJO band (wavenumbers 1–3 and 30–90-day periods), NCAR shows the lowest convergence–convection coherency among experiments, while COR3.0a-WAV exhibits the closest convergence–convection coherency to observations. Comparing COR3.0a with COR3.0a-WAV, the inclusion of waves generally enhances the convergence–convection coherency within the MJO band. This increased convergence–convection coherency is also present in the antisymmetric part at wavenumber 1, supporting the interpretation of more convectively coupled MJO behavior in COR3.0a-WAV.

4) Eastward and northward propagations

The eastward and northward propagation of the active convective center is an important feature of MJO activity and serves as an important metric for evaluating the model’s ability to accurately simulate the MJO (e.g., Wang and Oey 2008). Here, we will focus specifically on eastward propagation since northward propagation is more of a boreal summer feature. To analyze this feature, Fig. 8 shows lag–longitude diagrams of intraseasonal zonal winds at 850 hPa (contours) and precipitation (colors) in the equatorial region between 10°N and 10°S correlated against intraseasonal precipitation at a reference point in the Indian Ocean (80°–100°E) for boreal winter.

Fig. 8.
Fig. 8.

Lag–longitude diagram of 10°N–10°S-averaged precipitation (color) and U850 (contour) correlated against precipitation anomaly averaged over the reference region the Indian Ocean (10°N–10°S, 75°–100°E) during the extended boreal winter (November–April) for (a) TRMM and ERA5 wind 1998–2010 observations and (b)–(d) experiments.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

In observations (Fig. 8a), the key features of MJO eastward propagation are as follows: 1) a clear eastward propagation over the Eastern Hemisphere (EH) in both precipitation and U850 anomalies; 2) the precipitation anomaly is confined to the EH, and the U850 anomaly propagates faster in the Western Hemisphere (WH) after the decay of the precipitation anomaly near the date line; and 3) the U850 anomaly lags behind the precipitation anomaly by approximately 5–7 days. Common biases in models in simulating these observed features are present in all experiments (Figs. 8b–d), e.g., all experiments simulate a faster MJO speed, as compared to the observations. While COR3.0a (Fig. 8c) shows slightly better eastward propagation over the MC (100°–130°E, i.e., reduced barrier effects) than NCAR, the convective anomaly is more confined to the EH in NCAR (Fig. 8b). Nevertheless, both bulk algorithms exhibit weak eastward propagation of precipitation anomaly between 125°E and 180°. Comparing COR3.0a and COR3.0a-WAV (Figs. 8c,d), the presence of waves in the latter confines the convective anomaly to the EH by clearing off the excess precipitation in COR3.0a after the date line, and it also improves MJO propagation (more consistent and increased red color shading) across the MC up to the date line (180°). On balance, COR3.0-WAV suggests a modest improvement to some aspects of convection–circulation coupling compared to NCAR and COR3.0, mainly the reduced spurious positive precipitation anomaly signal along and east of the date line and the slightly less meandering positive precipitation signal between 120°E and 180°.

During the boreal summer season (May–October), the MJO is also characterized by northward propagation of intraseasonal anomalies in addition to eastward propagation (Waliser et al. 2009). Lag–latitude plots are used to diagnose northward propagation, analogous to lag–longitude diagrams for eastward propagation. For brevity, COR3.0a-WAV (Fig. S2) shows a slightly stronger and more coherent (less noisy) northward propagation.

5) Composite of MJO life cycle

Next, we assess the ability of different bulk algorithms to simulate the spatial-temporal structure of MJO-related ISV. Following the methodology described in Wheeler and Hendon (2004), Figs. 9 and 10 present the life cycle composite of MJO for both observation and experiments during the boreal winter season. It is constructed using the two leading pairs of principal components (PCs) obtained from a multivariate empirical orthogonal function (EOF) analysis of intraseasonal OLR and 850- and 200-hPa zonal winds averaged between 15°N and 15°S. The composite is based on only selecting days with PC12 + PC22 exceeding 1, which indicates strong MJO activity.

Fig. 9.
Fig. 9.

Extended boreal winter (November–April) composite 20–100-day OLR (color) and U850-hPa wind (vector) as a function of the MJO phase for (left) observations and (right) NCAR. The units (m s−1) of the reference vector and MJO phase number of days used to generate the composite are shown at the top and bottom right of each panel.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for (left) COR3.0a and (right) COR3.0a-WAV.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

In observations (Fig. 9a), the enhanced convective activity starts over Africa and the western Indian Ocean in phase 1, propagates eastward across the MC to the central Pacific, and dissipates in the eastern Pacific. Phases 2–3 and phases 6–7 of the MJO exhibit a stronger and more pronounced zonal dipole structure in tropical convection. In general, all bulk algorithms are able to adequately reproduce the observed sequence of MJO phases (Figs. 9b and 10a,b) although with a weaker magnitude of convection. However, there are certain biases and notable differences among the bulk algorithms in each phase, which are discussed below.

  • Phases 1–2: Both NCAR and COR3.0a show a dry bias in the western Indian Ocean (WIO) in phase 1 and overly strong easterlies across the eastern Indian Ocean (EIO) in phase 2. However, in COR3.0a-WAV, the presence of waves helps reduce these biases observed in COR3.0a.

  • Phases 3–4: Compared to the observed pattern, both NCAR and COR3.0a exhibit a wider longitudinal extent of convection anomalies and weak IO westerlies in phase 3, but COR3.0a shows stronger easterlies around the date line in phases 3 and 4. Waves in COR3.0a-WAV reduce the longitudinal extent of convection and stronger easterlies around the date line in phases 3 and 4, while increasing the magnitude of IO westerlies in phase 3, thus bringing COR3.0a-WAV closer to the observed patterns.

  • Phases 5–6: Here, both NCAR and COR3.0a exhibit overly strong westerlies and easterlies in the IO basin and Pacific Ocean (PO), respectively. They also show overly strong easterly anomalies across the tropical Atlantic Ocean, extending toward South America. The inclusion of waves in COR3.0a-WAV reduces these circulation biases. However, waves also lead to a further reduction in the overly weak convection in COR3.0a.

  • Phases 7–8: In NCAR and COR3.0a, easterlies in the Indian Ocean Basin and westerlies in the eastern to central Pacific Ocean are higher compared to observations. The inclusion of waves in COR3.0a-WAV reduces these circulation biases but again results in a further reduction in the excessively weak convection in COR3.0a.

In summary, NCAR and COR3.0a simulate very similar spatial structures and therefore share similar biases in convection and circulation anomalies. The presence of waves in COR3.0a-WAV reduces biases in circulation anomalies across all phases, which is consistent with the reduction in ISV in Fig. 4. As for convection, the waves primarily reduce biases over the IO basin, specifically the western IO, while slightly increasing them over the western PO. The phase–longitude relationship (not shown), which is analogous to the lag–longitude plot in Fig. 8, also shows that waves in COR3.0a-WAV effectively reduce the biases in convection anomalies observed in COR3.0a by clearing out the excess convection anomalies after the date line.

c. MJO column moist static energy analysis

The dynamics of MJO are governed by a recharge–discharge cycle, where column MSE accumulates before MJO deep convection takes place and is then released during and following MJO convection (Hendon and Liebmann 1990; Bladé and Hartmann 1993; Maloney and Hartmann 1998; Kemball-Cook and Weare 2001; Myers and Waliser 2003; Agudelo et al. 2006; Benedict and Randall 2007; Maloney 2009 and others). Analogous to Fig. 8, Fig. 11 shows lag–longitude diagrams of intraseasonal precipitation (lines), column-integrated moist state energy (m: colors, top row), and its tendency (m/t: colors, bottom row) correlated against precipitation at an Indian Ocean reference point for boreal winter.

Fig. 11.
Fig. 11.

Lag–longitude diagram of 10°N–10°S-averaged (top) column-integrated MSE (color) and (bottom) column-integrated MSE tendency (color) with precipitation (contour) correlated against precipitation anomaly averaged over the reference region the Indian Ocean (10°N–10°S, 75°–100°E) during the extended boreal winter (November–April) for observations (TRMM and ERA5 1998–2010) and experiments.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

As observed, the eastward propagation of column-integrated MSE anomalies 〈m〉′ is in agreement with the propagation of precipitation anomalies in both observation and experiments (Figs. 11a–d). Additionally, the MSE tendency term (Figs. 11e–h), which indicates moisture recharge and discharge before and during/after the MJO, respectively, also follows a similar pattern but 90° out of phase with the MSE anomalies, indicating positive (i.e., moistening) and negative (i.e., drying) tendency to the east and west of positive MSE anomalies, respectively.

Figure 11d shows that COR3.0a-WAV exhibits a more uniform positive precipitation (or MSE) signal stretching from the western Indian Ocean, particularly across the Maritime Continent, to the date line compared to the other experiments. Also, while the disruption of the MJO signal (or MSE) occurs further east than in observations, the COR3.0a-WAV experiment captures this disruption slightly more accurately than NCAR and COR3.0a. Thus, understanding the MJO recharge and discharge mechanisms of column MSE can provide insights into the underlying mechanisms driving differences between the bulk algorithms. Hence, we next analyze the MSE budget [Eq. (8)].

West of the date line (western PO, MC, and IO), horizontal and vertical MSE advection terms, with an opposing role from LHFLX anomalies, dominate the propagation (MSE tendency) of MSE anomalies preceding the MJO. However, these MSE advection terms contribute negatively to MSE maintenance during the MJO active phase, while LHFLX contributes to positive column MSE during this time (Fig. S4). The aforementioned MSE processes are in agreement with the findings of previous studies, such as Maloney (2009), Wolding et al. (2016), Ren et al. (2021), and Kim et al. (2022). On the other hand, both observations and experiments show that these MSE mechanisms break down near the date line, as the MJO begins to dissipate in the Western Hemisphere. To begin to understand what controls MJO propagation and maintenance across the date line in COR3.0a, we examine composite spatial patterns of each MSE budget term (Fig. 12).

Fig. 12.
Fig. 12.

Spatial distribution of MSE budget terms (W m−2) composited from MJO phases 4 and 5 for observation (ERA5) and experiments. The overlay contour represents the column-integrated MSE tendency term (m/t), while the overlay vectors represent winds at 850 hPa. The horizontal and vertical dashed black lines denote the equator and date line, respectively.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Following the peak MSE tendency around the date line during phases 4–5 (Fig. S3), Fig. 12 shows the composite (phases 4–5) spatial patterns of each term (color) contributing to the column-integrated MSE tendency (lines: m/t) preceding the MJO propagation across the date line. Note that column-integrated shortwave radiation heating and surface sensible heat flux are excluded as they are an order of magnitude lower than column-integrated longwave radiative heating and surface LHFLX, respectively. Observations and experiments show a zonally asymmetric MSE tendency (m/t) with a positive tendency anomaly to the east and negative anomaly to the west of the western Pacific Ocean and a particularly strong positive tendency in the eastern Pacific Ocean.

East of the date line, observations show that LHFLX is a dominant factor for the eastward propagation of the MSE anomalies, with the largest opposing contribution from the horizontal advection term, which is reversed relative to the west of the date line. The dominant MSE budget terms, LHFLX and horizontal advection, which contribute to the tendency in all three experiments generally follow similar patterns as shown in the observations. However, NCAR and COR3.0a algorithms tend to overestimate the LHFLX anomalies around 180°–150°W, with COR3.0a showing a larger overestimation. The inclusion of waves in the COR3.0a-WAV algorithm results in a reduction of the overestimated LHFLX anomalies, bringing them closer to the observed values (fourth column in Fig. 12). The circulation anomaly patterns during the MJO propagation east of the date line (phases 4–5) in Fig. 9 suggest that the overly strong LHFLX anomalies in COR3.0a (Fig. 12: third column, fifth row) are directly linked to an overestimation of surface easterly anomalies.

In terms of MSE maintenance, the MSE anomalies around the date line peak during phases 7 and 8 (6 and 7) in observations (experiments). Figure 13 shows the composite spatial patterns of each term (color) contributing to the column-integrated MSE (lines: 〈m〉′) when the MJO is near the date line. The dominant balance along and east of the date line is between LHFLX and horizontal MSE advection as in the MSE tendency. However, in this case, horizontal MSE advection is positively correlated with column-integrated MSE, while LHFLX is negatively correlated with column-integrated MSE. As in the MSE tendency, NCAR and COR3.0a overestimate both terms, with COR3.0a showing a larger overestimation. Overestimation results in slightly higher MSE anomalies north of the equator in the longitude range 180°–150°W than observed. In COR3.0a-WAV, the presence of waves slightly reduces the higher MSE anomalies seen in COR3.0a. This is achieved by reducing the horizontal MSE advection, which otherwise acts to moisten the column in this phase of MJO. The positive bias observed in horizontal MSE advection in COR3.0a and NCAR might be due to a more anomalous poleward flow, potentially advecting/spreading abundant equatorial moisture poleward (e.g., compare Figs. 9 and 10 phase 7 around 140°W; 10°N). Horizontal MSE advection in COR3.0a-WAV is weaker due to the more zonal flow (Fig. 10 phase 7; second column).

Fig. 13.
Fig. 13.

Spatial distribution of MSE budget terms (W m−2) composited from MJO phases 7 and 8 for observation (ERA5) and phases 6 and 7 for experiments. The overlay contour represents the column-integrated MSE term (〈m〉′). The horizontal and vertical dashed black lines denote the equator and date line, respectively.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Near the date line, we also estimate the relative contribution of each MSE budget term to the maintenance and propagation of MSE anomalies by projecting them upon MSE anomalies and their tendencies (Fig. S5) following Andersen and Kuang (2012). Consistent with the conclusions drawn from Figs. 12 and 13, the moistening effect of the LHFLX during phases 4–5 (propagation) and that of horizontal advection during phases 6–7 (maintenance) are strongly overestimated in COR3.0a. The inclusion of waves in COR3.0a-WAV reduces the biases.

Figure 14 shows the boreal winter (DJF) mean state of LHFLX, winds at 850 hPa and wind stress in COR3.0a, and its differences from COR3.0a-WAV (i.e., COR3.0a-WAV-COR3.0a). To facilitate the explanation of the observed changes, two boxes were selected: one to the left and one to the right of the date line (180°). In COR3.0a, zonal wind stress (color: Fig. 14a) in the right (left) box is dominated by easterlies (westerlies). Waves in COR3.0a-WAV induce basinwide westerlies (Fig. 14a: blue contour), thereby reducing the easterlies in the right box and increasing westerlies in the left box. Similar changes are seen in the 850-hPa winds (Figs. 14c,d). These boxes are centered at the transition point from westerlies to easterlies, thus resulting in significant wind variation within the box. In the right box, the drag coefficient difference between NCAR and COR3.0a is nearly zero. Hence, the slightly stronger wind stress in COR3.0a than NCAR results from the enhanced low-level wind in COR3.0a, which is probably produced by other atmospheric processes, such as the pressure gradient. By simulating higher values of the Charnock parameter αw than COR3.0a, waves in COR3.0a-WAV estimate higher drag coefficients over the basin, consequently reducing the strong easterlies simulated in COR3.0a.

Fig. 14.
Fig. 14.

COR3.0a boreal winter mean of (a) wind stress (vector) and zonal wind stress (color). The overlay blue contour is the mean zonal wind stress difference between COR3.0a and COR3.0a-WAV (i.e., COR3.0a-WAV–COR3.0a). (b) Differences in surface LHFLX (color) and wind stress (vectors) between COR3.0a and COR3.0a-WAV. (c) As in (a), but with 850-hPa wind; (d) as in (b), but with 850-hPa wind. The location of the green boxes are left: 15°–35°N and 130°–170°E, right: 15°–35°N and 160°–120°W. Thick white arrows represent the mean wind direction in each box. The horizontal and vertical dashed black lines denote the equator and date line, respectively.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

In summary, the simulated stronger mean state easterlies over the Pacific Ocean basin in COR3.0a compared to COR3.0a-WAV suggests a highly convergent flow with large surface convergence near the equator. This condition would generally promote more rapid and robust MJO eastward propagation, especially if Kelvin wave–induced anomalous easterlies are added to the mean state easterlies. The inclusion of waves in COR3.0a-WAV weakens these low-level easterlies in COR3.0a, leading to a weakening of the boundary layer convergence effect, which subsequently hinders the MJO propagation east of the date line. Thus, the stronger boundary layer frictional convergence and wind–evaporation feedbacks explain why MJO convection propagates more strongly across the central/eastern Pacific in COR3.0a.

5. Summary and discussion

In this study, we investigated the effect of the choice of surface flux parameterization on MJO by performing two experiments with wind speed–dependent bulk algorithms, NCAR and COARE3.0a (as COR3.0a), and one experiment with wave-state-dependent flux (COR3.0a-WAV). All experiments followed the CMIP6 preindustrial control run.

NCAR (Large and Yeager 2009) and COARE 3.0a (Fairall et al. 2003) bulk formulas are the two widely used flux parameterizations in GCMs. Differences in the parameterizations arise from the approximation of neutral drag coefficients CDN which are reflected in the computation of wind stress and latent and sensible heat fluxes. These traditional bulk formulas assume that the surface winds are in equilibrium with the waves, and therefore a continuity of momentum (fluxes) at the air–sea interface. However, in reality, waves propagate faster than winds and sometimes in different directions, thus, not always in equilibrium with the surface winds. As waves grow or decay, the stress on the ocean side τocn increases or decreases relative to the airside stress τatm. The physics of the air–sea coupling depends on surface wave conditions such as growth and dissipation. To account for wave-state-dependent air–sea fluxes, we implemented WAVEWATCH III in E3SM and coupled its state to the atmospheric and ocean model components. We modified the COARE3.0a algorithm by incorporating the Charnock parameter calculated within the WW3 model and also accounted for the buffering effect of surface waves on the relative difference between τocn and τatm.

Through these experiments, we hope to contribute to the understanding of how the choice of surface flux parameterization and proper representation air–sea coupling through the integration of surface waves in GCMs affect the simulation of the MJO. The main results are as follows.

  1. Differences do exist between these experiments and observations in the mean climate during the extended boreal winter (November–April). The MJO is sensitive to changes in mean state (Inness and Slingo 2003; Ahn et al. 2020; DeMott et al. 2019; Henderson et al. 2017). The notable differences in mean climate are as follows:

    • NCAR and COR3.0a underestimate easterly wind stress in the tropical Pacific Ocean (Fig. 2a-5). However, COR3.0a simulates stronger easterlies than NCAR and the surface waves (COR3.0a-WAV) reduce the strong easterlies (Fig. 2a-6) in COR3.0a by simulating higher drag coefficients. It is important to note that the dependence of observation-based products on similar bulk algorithms as GCMs makes it difficult to determine whether the observation overestimates or the GCMs underestimate easterly wind stress (Simpson et al. 2018).

    • All experiments simulate more evaporation (stronger latent heat flux) than observed (Figs. 2b-2b-4). COR3.0a exhibits less evaporation than NCAR in most regions (Fig. 2b-5). This is apparent from COR3.0a’s lower moisture transfer coefficients (Fig. 1). However, due to an air–sea feedback, LHFLX differences among experiments are also driven by wind stress–induced changes in some regions. Changes in LHFLX due to surface waves modification are up to 5%–10%.

    • SST in COR3.0a is warmer compared to NCAR (Fig. 2c-5), and waves amplify the warming (Fig. 2c-6) in the tropical Pacific Ocean with an El Niño–like pattern. SST changes are predominantly controlled by the LHFLX changes in most regions (Bonino et al. 2022). However, in a coupled simulation where surface winds vary, SST changes are also influenced by wind stress–induced changes in the upper ocean dynamics such as entrainment, vertical advection, and mixing.

  2. The basic spatial distribution pattern of intraseasonal variance (ISV) in OLR and U850 is well represented relative to observations in all experiments (Fig. 4). NCAR and COR3.0a share similar strong ISV biases in U850 and OLR, with COR3.0a showing a higher overestimation. It should be acknowledged, however, that many current GCMs also exhibit similar strong ISV biases (e.g., Kim et al. 2009). However, the inclusion of waves in COR3.0a-WAV reduces the strong ISV biases, especially around the MC and central Pacific (Figs. 4a-6,b-6). The unfiltered mean variance of OLR and U850 follow the same patterns of bias and differences between experiments as in ISV.

  3. All experiments show weaker MJO convection–circulation coupling than observed (Fig. 7). COR3.0a demonstrates stronger coupling than NCAR, but the addition of waves in COR3.0a-WAV further intensifies the convection–circulation coupling in COR3.0a. The magnitude of the MJO circulation anomaly in both NCAR and COR3.0a (Figs. 9 and 10) tends to be either amplified (e.g., phase 5) or reduced (e.g., phase 3). Waves, however, adjust the circulation anomaly back toward the observed magnitude.

  4. NCAR exaggerates the barrier effect of the MC on MJO propagation than COR3.0a, although both exhibit weak eastward MJO propagation between 125°E and 180° (Fig. 8). In COR3.0a, the MJO propagates east of the date line into the eastern Pacific Ocean with a weak convection anomaly. Waves in COR3.0a-WAV slightly improve MJO propagation over the MC and between 125°E and 180° and confines the MJO to the EH by eliminating the excess convective anomaly seen after the date line in COR3.0a (Fig. 8d).

  5. MSE budget analysis revealed that the excessive LHFLX and horizontal advection of MSE (Hadv) anomalies are responsible for the propagation and maintenance of the MJO east of the date line, respectively, in COR3.0a (Figs. 1113), which is in contrast to their respective roles west of the date line (Maloney 2009; Wolding et al. 2016; Ren et al. 2021; Kim et al. 2022). The excess LHFLX and Hadv anomalies in COR3.0a simulation stem from COR3.0a’s simulated high mean state easterlies over the Pacific Ocean basin. Through the wind-induced surface heat exchange (WISHE) mechanism (Emanuel 1987), the reduction of easterlies by waves results in a corresponding decrease in LHFLX and Hadv anomalies (Fig. 14). This consequently reduces boundary layer moisture convergence and confines MJO to the Eastern Hemisphere in the COR3.0a-WAV simulation.

We have shown that the choice of bulk algorithm can result in changes in simulated MJO characteristics. Our results suggest that differences in bulk algorithms across GCMs may contribute to the intermodel spreads (Chen et al. 2022) observed in MJO characteristics within the CMIP6 models. It is also natural to expect that the choice of bulk algorithm will affect MJO’s response to future climate changes. The choice of the bulk algorithm also influences MJO teleconnection patterns, as these patterns are sensitive to changes in the mean state (Henderson et al. 2017; Zheng and Chang 2020) and propagation (Bladé and Hartmann 1995; Wang et al. 2020) characteristics of the MJO itself. To illustrate the influence of surface flux parameterization on MJO teleconnection amplitude and patterns, Fig. 15 shows the teleconnection patterns associated with MJO phase 3, which is one of the most effective MJO phases in exciting extratropical circulation anomalies (Henderson et al. 2017). While it is clear that the MJO teleconnection patterns in all experiments have many differences from observations, surface flux changes lead to significant changes in teleconnection patterns among experiments. Further simulations and in-depth analysis are needed to understand these differences in the MJO teleconnection patterns.

Fig. 15.
Fig. 15.

MJO phase 3 pentad (5-day lag mean) composites of anomalous 250-hPa geopotential height (contour) and anomalous precipitation (color) composite during MJO phase 3. Contours are every 10 m, and the zero contour is omitted. Black stippling denotes anomalies that are 95% significant.

Citation: Journal of Climate 37, 10; 10.1175/JCLI-D-23-0490.1

Our study provides additional evidence of the significance of background state in simulating a realistic propagation of intraseasonal anomalies. Most importantly, we show that the proper treatment of air–sea coupling via the inclusion of wave-induced effects generally improves the simulation of the MJO. This could be a significant step toward improving MJO simulations, even though numerous challenges still exist (e.g., Zadra et al. 2018). This is the first study to investigate the impacts of ocean surface waves beyond the atmosphere–ocean interface, and more work needs to be done to reveal the dynamical pathway(s) through which surface waves modify coupled climate variability. The wave effects here are only a small set of wave processes important to coupled ocean–atmosphere variability. In addition to the wave-state momentum flux addressed in this study, it is important to consider other wave-induced effects such as Stokes drift and sea spray in surface flux parameterization. Stokes drift modifies the air–sea relative speed during air–sea flux calculations, while sea spray modifies the turbulent heat fluxes as water droplets from breaking waves exchange moisture and mass with the atmosphere. Further efforts are required to integrate all wave-induced effects (including wave state momentum flux, Stokes drift effects, and sea spray effects) into the calculation of surface turbulent fluxes, thus transitioning from an air–sea to an air–wave–sea bulk parameterization. Using historical simulations and future projections, future studies should explore the impacts of bulk algorithm choice on MJO properties such as propagation, intensity, teleconnection patterns, number of events, MJO–ENSO interactions, and MJO–IOD interactions.

Acknowledgments.

This research was supported as part of the Energy Exascale Earth System Model (E3SM) project, funded by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research. This research used resources from the Argonne Leadership Computing Facility at the Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract DE-AC02-05CH11231. We would also like to acknowledge the use of NCAR’s Cheyenne and Casper supercomputers (https://doi.org/10.5065/D6RX99HX, CISL, 2019), which is supported by the National Science Foundation. OJI would like to thank the United Nations Intergovernmental Panel on Climate Change (IPCC) Scholarship. YD is in part supported by the U.S. National Science Foundation (NSF) through Grant AGS-2032532 and by the U.S. National Oceanic and Atmospheric Administration (NOAA) through Grants NA20OAR4310380 and NA22OAR4310606.

Data availability statement.

All the observational datasets used in this study are listed in the references. The E3SM source code is publicly available on GitHub: https://github.com/E3SM-Project/E3SM (last access: 2 May 2023).

APPENDIX

Equations

a. Drag/transfer bulk coefficients

The drag/transfer bulk coefficients are defined as
CD,E,H=κ2[log(zmzo)ψm,e,h][log(zm,e,hzo)ψm,e,h].

b. Stress calculated from the 2D wave spectrum

Stress from the 2D wave spectrum is calculated as
τwavatm=ρwg02π0kωSindωdθ,
τocnwav=ρwg02π0kωSdsdωdθ,
where τwavatm is the wave-supported stress: input stress from the atmosphere to the wave (for growing), τocnwav is the dissipation stress from the wave to the ocean (always negative), Sin is the wind input source term, Sds is the dissipation source term (momentum sink for the wave field), ρw is the water density, θ is the wave direction, ω is the absolute frequency, and k is the wavenumber.

c. Evolution of the wave action density in WW3

The evolution of wave action density in WW3 is given by
Nt+(CϕN)ϕ+(CλN)λ+(CσN)σ+(CθN)θ=iSi.
Equation (A4) is solved by discretizing in both physical space (λ, ϕ) and spectral space (σ, θ). Here, N is the action density, ϕ is the longitude, λ is the latitude, σ is the relative frequency, θ is the direction, Cσ and Cθ are the wave propagation velocity in spectral space (σ, θ), Cϕ and Cλ are the wave propagation velocity in the (ϕ, λ) direction, t is the time, and S represents the source and sink terms.

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