Diagnostic Method for Atmosphere–Ocean Coupling Over Tropical Oceans at the Sub‐Seasonal Timescale

This study introduces a novel diagnostic method to assess tropical atmosphere‐ocean coupling, using a two‐dimensional plane defined by the 90‐day high‐pass‐filtered sea surface temperature (SST) and column water vapor (CWV). The method was applied to reanalysis data and high‐resolution coupled atmosphere‐ocean simulation data. In the Indo–Pacific warm pool region, the phase relationship between SST and CWV remained consistent across both reanalysis and simulation data sets. However, differences in the temporal evolution of these variables were observed in the central Pacific region. The heat budget analysis results indicate that the differences between the two data sets in the central Pacific are related to variations in the effects of atmospheric disturbances on SST. This study demonstrates the potential of our novel diagnostic method for evaluating atmosphere–ocean coupling in climate models.


Introduction
Atmosphere-ocean interactions in the tropics can be observed at various time scales.Lead-lag correlations between precipitation and sea surface temperature (SST), as well as simultaneous correlations between precipitation and SST tendencies, have been employed to explore regional differences in atmosphere-ocean interactions.On the seasonal scale, simultaneous correlations between precipitation and SST are pronounced in the eastern Pacific due to the El Niño-Southern oscillation, whereas in the Indo-Pacific warm pool, the precipitation peak typically lags behind the SST peak (von Storch, 2000;Arakawa & Kitoh, 2004;Trenberth & Shea, 2005;Wu et al., 2006;Wu & Kirtman, 2007;Kumar, Chen, & Wang, 2013).Even on the intraseasonal (20-90-day) scale, the precipitation peak lags behind the SST peak in the Indo-Pacific warm pool (Arakawa & Kitoh, 2004;Kumar, Zhang, & Wang, 2013), possibly linked to intraseasonal oscillations such as the Madden-Julian oscillation (Lau & Sui, 1997;Woolnough et al., 2000) and the Asian monsoon (Roxy et al., 2013).The lead-lag correlations between precipitation and SST and simultaneous correlations between precipitation and SST tendencies have also been used to evaluate the reproducibility of tropical precipitation and SST in climate models (Wu et al., 2006(Wu et al., , 2013;;Yang & Huang, 2023).
In recent years, there has been a significant push toward developing high-resolution atmosphere-ocean coupled models to represent the interactions between atmospheric moist convection and the ocean (e.g., Hohenegger et al., 2023;Miyakawa et al., 2017).Consequently, diagnostic methods are needed to evaluate the sub-seasonal (2-90-day) atmosphere-ocean variability, encompassing the synoptic timescale (2-20-day) variability, which is a focus of the high-resolution models.Previous investigations into subseasonal lead-lag relationship (Roxy et al., 2013;Wu, 2019;Wu et al., 2008;Ye & Wu, 2015) have primarily concentrated on the Indo-Pacific warm pool and overlooked regional distinctions within the tropics.Additionally, it is essential to delineate how these changes align with specific atmospheric disturbances such as convectively coupled equatorial waves.Moreover, it is imperative to elucidate the processes through which atmospheric disturbances affect SST, including windevaporation, cloud-radiation, and wind-induced oceanic mixing and upwelling effects.
We adopt an alternative approach to model evaluation compared to the lead-lag correlation method.Diagnostic methods have been proposed to delineate the convection life cycle by examining the time evolution of the two variables involved in convection on a plane (Inoue & Back, 2017;Wolding et al., 2022).The relationship between convection and SST has also been explored using the SST-column water vapor (CWV) plane (Kanemaru & Masunaga, 2013) and the SST-precipitation plane (Wu, 2019).In this study, by assessing the vector field of tendencies on the SST-CWV plane, we depict a life-cycle representation of atmospheric convection interacting with the ocean.An advantage of analyzing tendencies is that the impact of atmospheric disturbances on SSTs can be evaluated through a mixed-layer heat budget analysis.
This study shows the potential of the proposed diagnostic method for assessing differences across data sets in atmosphere-ocean interactions at the sub-seasonal scale.The temporal evolution depicted in the SST-CWV diagram, derived from the reanalysis data and the high-resolution coupled simulation data, clearly illustrates differences between regions and data sets.Furthermore, through integration with the lag composite and the heat budget analysis, we identify atmospheric disturbances corresponding to the temporal evolution depicted in the diagrams and the processes contributing to the differences in the temporal evolution.

Satellite and Reanalysis Data
We used the NOAA 1/4°daily Optimum Interpolation Sea Surface Temperature (OISST) v2 data set (Huang et al., 2021) to investigate sub-seasonal time variability of SST.The satellite SST data source input to OISST switched from the Pathfinder Advanced Very High Resolution Radiometer (AVHRR) SSTs to Operational Navy SSTs as of 2007.Because the characteristics of the SST variability after 2007 changed due to the change in input source, the data from years 2007 and later are used in the analysis.
To evaluate the mixed layer depth (MLD), we used the NCEP Global Ocean Data Assimilation System (GODAS) data set (Huang et al., 2010).GODAS provides pentad (5-day) mean temperature and salinity on a 1/3°latitude by 1°longitude grid in the tropical region.MLD was defined as the depth at which the potential density exceeds nearsurface potential density by 0.03 kg m 3 .Daily MLD values were derived by interpolating the pentad GODAS values on a daily basis.Some studies define MLD as the depth where the water temperature is 0.2°C lower, approximately 20 m deeper than the above definition, owing to barrier layers in the tropics ( de Boyer Montégut et al., 2004).
The daily mean CWV was computed by averaging the instantaneous values at 00, 06, 12, and 18 UTC from the ERA5 reanalysis data set (Hersbach et al., 2020).Similarly, the daily precipitation, latent heat, sensible heat, and net radiation fluxes at the surface were also computed from the ERA5 reanalysis data set by averaging.
To filter out the mesoscale variations associated with atmospheric convection and to concentrate on sub-seasonal timescale variations, spatial averaging was applied to coarsen all the data to a 1°horizontal grid.The analysis period spanned from 2007 to 2020, during which all the data sets were uniformly available.For simplicity, these data sets, including OISST, are collectively referred to as "reanalysis data."

Atmosphere-Ocean Coupled Simulation Data
We conducted experiments using the high-resolution atmosphere-ocean coupled general circulation model, NICOCO (Miyakawa et al., 2017).The atmospheric component of this coupled model was the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) (Kodama et al., 2021;Tomita & Satoh, 2004).The simulation was performed on a 14 km horizontal mesh.The model had 78 vertical levels, with the lowest level at 33 m and the uppermost level at 50 km.We provided data from ERA5 on 1 January 2010, as the initial values for the simulation.The model settings were the same as those described in Kodama et al. (2021), but without the external forcing by volcanic aerosols.Specifically, the model used a single-moment bulk cloud microphysics scheme with six water categories (Roh et al., 2017;Tomita, 2008) and did not use any cumulus convection schemes.
The ocean component of the model is the CCSR Ocean Component Model (COCO) (Hasumi, 2006), with a horizontal grid size of 0.25°, which is finer than the mesh that is generally used for climate simulations (Tatebe Geophysical Research Letters 10. 1029/2023GL106837 et al., 2019)).Initial conditions were generated from a stand-alone run of COCO, wherein the climatology of the water temperature and the salinity from the World Ocean Atlas 2013 (Boyer et al., 2013) was incorporated, with current velocities initialized to zero.Subsequently, the ocean interior was spun up by integrating under the boundary conditions of the Japanese 55-year atmospheric reanalysis designed for driving ocean and sea ice models (JRA55-do) (Tsujino et al., 2018) from 1958 to 2010.
The atmospheric and oceanic models were coupled using a coupler, Jcup (Arakawa et al., 2011), with a coupling interval of 20 min.The NICOCO integration started from January 2010.In subsequent analyses, we used the sixyear simulation data from January 2011 to December 2016.To filter out the mesoscale variability associated with atmospheric convection, the daily mean values were computed from the original hourly averaged output values and were coarsened to a 1°horizontal grid for the analysis.

The SST-CWV Diagram
To display how the atmosphere and the ocean fields interact and evolve at a sub-seasonal time scale, we focused on the 90-day high-pass-filtered SST (hereafter denoted as T′) and CWV (hereafter denoted as W′), as well as their respective tendencies (∂T′/∂t and ∂W′/∂t).In the two-dimensional plane spanned by T′ and W′, each point reflected the atmospheric and oceanic conditions at a specific time and location.The tendencies of T′ and W′ calculated from data was averaged within bins in the T′-W′ plane, with T′ divided into bins of width 0.25 K and W′ divided into width 2.5 kg m 2 .Because our focus was on sub-seasonal variation, the tendency of T′ was defined as the difference between the T′ values one day after and one day before a target date.The definition was the same for the tendency of W′.The averaged tendencies of T′ and W′ computed for the various bins in the T′-W′ plane constituted a vector field.Hereafter, the diagram plotting the tendency vectors in the T′-W′ plane is referred to as the SST-CWV diagram.We conducted a comparative analysis of two tropical ocean regions: the equatorial warm pool (WP; 5°S-5°N, 60°E 160°E) and the central Pacific intertropical convergence zone (CP; 0-10°N, 160°E 150°W).
We introduced a metric representing the rotational time evolution on the T′-W′ plane for each 10°× 10°region.This metric is called mean angular velocity and was calculated as follows: First, the angular velocity around the origin was calculated from the vector representing the tendencies of T′ and W′ for each bin in the T′-W′ plane.To calculate the angular velocity, we set the scale of the T′-axis to 1 K and the W′-axis to 10 kg m 2 , ensuring that the variances of the two variables were comparable.Then, a weighted average of the angular velocity by the number of data across bins in the T′-W′ plane was calculated.For a detailed calculation methodology, please refer to supporting information Text S1 and Figure S1 in Supporting Information S1.

Lag Composite Analysis
A lag composite analysis was conducted to elucidate the atmospheric disturbances associated with the time evolution on the SST-CWV diagram.Using the time series of W′ at the location of 180°, 5°N as a reference, peaks with magnitudes exceeding one standard deviation were identified.Composites were constructed at three time points: one day before (Day 1), the reference day (Day 0), and one day after (Day 1).
To investigate the processes contributing to the tendency of T′, we assessed the forcing term based on the following equation for the ocean mixed-layer heat budget along the zonal section at 5°N on Day 0: where C pw is the constant pressure specific heat of seawater, ρ w is the density of seawater, and H ML is the mixed layer thickness.The low-pass-filtered component of the total tendency of the SST was ignored here because it is sufficiently small relative to the high-pass-filtered component.Q rad is the net radiation flux, which includes both the longwave and shortwave radiation at the surface.Q LH+SH is the sum of the latent and sensible heat fluxes.Q res is the residual term; it is calculated from the other terms and includes internal ocean processes, such as vertical mixing and horizontal advection.

SST-CWV Diagram
The SST-CWV diagrams for the WP and CP regions are shown in Figure 1.Interestingly, the time evolutions of T′ and W′ derived from the reanalysis data exhibit distinct characteristics between these regions.In the WP region (Figure 1a), the vector field of the tendencies of T′ and W′ exhibits counterclockwise rotation around the origin, indicating that the SST maxima precede the CWV maxima.Conversely, in the CP region (Figure 1b), the rotation was clockwise, signifying that the CWV maxima preceded the SST maxima.However, the SST-CWV diagrams from the NICOCO simulation data illustrated in Figures 1c and 1d demonstrate counterclockwise rotation in both the CP and WP regions, which differs from the reanalysis data in the CP region.Note that the vector of the tendencies of T′ and W′ strongly reflects the change in the shorter-period components of T′ and W′.
In both the reanalysis and simulation data, the CWV peak lagged behind the SST peak in the WP region, which is consistent with previous studies that noted that the precipitation peak lags behind the SST peak (Roxy et al., 2013;Wu, 2019;Wu et al., 2008;Ye & Wu, 2015).The SST-CWV diagram is thought to visualize the following picture related to the life cycle of atmospheric convection: as SST increases, instability increases and convection becomes more active, and in turn, convective activity lowers SST by modulating radiation and surface fluxes (Roxy et al., 2013).On the other hand, limited research has been conducted on the temporal evolution of SST and CWV in the CP region, where differences between the data sets have been identified.Because NICOCO exhibits model biases and SST data sets generally has uncertainty in its ability to reproduce short-term SST variability (Kumer et al., 2013a), it remains unclear which data set better represents reality.To explore the spatial distribution of the different time-evolution regimes within the SST-CWV diagram derived from the reanalysis data, Figure 2a illustrates the mean angular velocities calculated for the 10°× 10°regions.The time-evolution exhibits a counterclockwise rotation in the WP region (the red box), while it manifests clockwise in the CP region (the blue box).The lead-lag correlation analysis using pentad data of SST and precipitation of Arakawa and Kitoh (2004) shows that the precipitation peak lags behind the SST peak in the WP region, but the lag relationship is unclear in the CP region.Our results are in general agreement with their findings, highlighting the spatial contrast in the time-evolution regimes more distinctly.Conversely, data from the NICOCO simulation shown in Figure 2b indicate a counterclockwise rotation in the tropical regions characterized by high precipitation rates and SSTs exceeding 28°C.

Lag Composite Analysis
A lag composite analysis was used to investigate the differences between data sets in the temporal evolution of SST and CWV in the CP region and their association with atmospheric disturbances.Figure 3 shows the lag composite diagram based on the peaks of W′ at 180°and 5°N.In both data sets, a positive W′ propagates westward, with southwesterly winds traversing the equator toward the disturbance center.This disturbance observed in the central Pacific is related to mixed Rossby-gravity (MRG) wave-type disturbances (Takayabu & Nitta, 1993).
While the structure of the disturbances is similar between the data sets, the SST responses are different.In the reanalysis data, negative T′ was observed near the reference point (180°, 5°N) on Day 1 (Figure 3a), then T′ increased with time, and the region of statistically significant negative T′ nearly dissipated on Day 1 (Figure 3c).Conversely, in the NICOCO simulation data, a positive T′ is observed near the reference point on Day 1 (Figure 3b), but T′ decreases with time, becoming negative on Day 1 (Figure 3f).These temporal changes in SST are consistent with the SST tendencies in the regions with high CWV in the SST-CWV diagrams illustrated in Figures 1b and 1d.
To elucidate the reasons for the differences in the SST tendencies as disturbances passed between data sets, an ocean mixed-layer heat budget analysis was conducted along the 5°N zonal section.In the reanalysis data, the SST tendency shown by the black line in Figure 4b was positive, corresponding to disturbances associated with positive W′ as indicated by the blue line in Figure 4a.Examining the breakdown of this tendency in Figure 4c, it is primarily the residual term (blue line) that contributes to heating, which is partially offset by cooling due to the radiative term (red line).It is important to note that the ratio of the residual term to the other two terms is subject to uncertainty owing to the variations in the MLD in the denominator of Equation 1 owing to differences in the definitions and data used.
Despite uncertainties in the contribution of the heating terms owing to the estimation of the MLD, the following hypothesis can be made about the mechanism by which the residual term increases SST: the negative anomaly in the 10 m wind speed, depicted by the orange line in Figure 4e, indicates that cooling due to vertical mixing within the ocean might have been weakened, contributing to heating by the residual term.This negative anomaly in the 10 m wind speed stems from the weakening of the background northwesterly winds (not shown) by the southwesterly wind anomaly associated with the disturbance seen in Figure 3c.This hypothesis, positing that SST cooling due to vertical mixing in the ocean mixed layer is controlled by disturbance-induced changes in 10 m wind speed, explains the clockwise time evolution in Figure 1b.
As observed in Figures 4b and 4d, negative SST tendencies were noted in the NICOCO simulation data in association with disturbances related to positive W′.The heat budget analyses depicted in Figure 4d indicate that the negative tendency primarily results from cooling by the radiative term, with the latent and sensible heat terms partially contributing to the cooling on the eastern side of the disturbance.The residual term was smaller than these two terms, possibly because the NICOCO MLD (Figure 4f) was shallower than the reanalysis MLD (Figure 4e).It is thought that the following process is dominant in this region: when atmospheric convection is active, the insolation of shortwave radiation decreases and the SST tendency is negative, and conversely, when atmospheric convection is inactive, the insolation of shortwave radiation increases and the SST tendency is positive.This process elucidates counterclockwise time evolution shown in Figure 1d.

Summary
We proposed a diagram to visualize the time evolution of the 90-day high-pass-filtered SST and CWV data in a two-dimensional plane to assess sub-seasonal atmosphere-ocean interactions associated with atmospheric convection.The SST-CWV diagram derived from the reanalysis data for the equatorial warm pool region exhibited a counterclockwise rotation of the vector field of tendencies, indicating that the SST maxima preceded the CWV maxima.Conversely, the SST-CWV diagram for the tropical central Pacific depicted a clockwise rotation of the vector field of tendencies.Analyses using high-resolution simulation data from NICOCO showed a counterclockwise rotation throughout the tropics, with high precipitation and SSTs above 28°C.As demonstrated, the SST-CWV diagram can effectively elucidate the differences in the atmosphere-ocean coupling between regions and data sets at the sub-seasonal timescale.
We conducted a lag composite analysis to explore the discrepancies between the data sets in the temporal evolution of SST and CWV in the equatorial central Pacific region and their association with atmospheric disturbances.Both data sets showed westward-propagating disturbances that shows the characteristics of MRG wave- type disturbances, but the SST responses differed.In the reanalysis data, the SST increase primarily stemmed from the residual term, possibly due to weakened cooling from vertical mixing in the ocean caused by the decreased 10 m wind speed.Conversely, in the NICOCO simulation data, the SST decrease mainly resulted from the radiation term, likely attributed to solar insolation being intercepted by clouds.The differences in the time evolution of the SST-CWV diagrams reflect the differences in the processes by which atmospheric disturbances impact SSTs.
To correctly interpret the differences in the SST-CWV diagrams observed in the central Pacific, verifying whether the multiday-scale variability observed in the OISST can serve as ground-truth data for model evaluation is imperative.Kumar, Zhang, and Wang (2013) highlighted differences in the SST-precipitation relationship depending on the SST data set.Consequently, we plan to conduct analyses using in situ data from moored buoys.
Studying atmosphere-ocean interactions on an intraseasonal scale can be facilitated by applying a band-pass filter that cuts out the synoptic timescale components of SST and CWV.For instance, SST variations have been demonstrated to respond to atmospheric disturbances such as equatorial Rossby waves and equatorial Kelvin waves (Nakamura & Takayabu, 2022), as well as the Madden-Julian oscillation (e.g., DeMott et al., 2015).Additionally, SST variability associated with tropical instability waves in the tropical Atlantic and Pacific, which are known to be related to surface winds (Chelton et al., 2001) and the cloud cover (Deser et al., 1993), receives feedback from the atmosphere (Seo et al., 2007).

Figure 1 .
Figure 1.SST-CWV diagrams.A 90-day high-pass filter is applied to the SST and CWV data.The arrows represent the tendency vectors of SST and CWV in each bin, and their length represents the amount of change over 5 days.The contours show the frequency of existence with values of 10 4 , 10 3 , and 10 2 .Panels (a) and (b) are derived from OISST and ERA5 data from 2007 to 2020, whereas panels (c) and (d) are derived from NICOCO simulation data.Panel (a) and (c) represents WP, and panels (b) and (d) represents CP.Only bins in which the tendencies of SST and CWV are statistically significantly different from 0 at the 5% significance level and with a sample size of 100 or greater are shown.

Figure 2 .
Figure 2. Spatial distribution of the mean angular velocity of the tendencies in the SST-CWV diagram.Positive (negative) values indicate counterclockwise (clockwise) rotation.Contours with SSTs of 28°C, 29°C, and 30°C are also shown.Panel (a) is derived from the OISST and ERA5 data, whereas panel (b) is derived from the NICOCO simulation data.The red and blue boxes shown in panel (a) represent the WP and CP regions, respectively.

Figure 3 .
Figure 3. Lag composite based on maxima greater than 1σ of the CWV time series at 5°N, 180°E.Vectors represent wind at 10 m above ground, contours represent CWV, and color shading represents SST; only 95% significant data are shown.A 90-day high-pass filter was applied to all variables.Panels (a), (c), and (e) are derived from the OISST and ERA5 data, whereas panels (b), (d), and (f) are derived from the NICOCO simulation data.(a) and (b) represent Day 1, (c) and (d) represent Day 0, and (e) and (f) represent Day 1.

Figure 4 .
Figure 4. Cross section at 5°N for Day 0. Panels (a) and (b) show SST and CWV.respectively.Panels (c) and (d) show the SST tendency (dSST) and heating rates due to Q rad ,Q LH+SH and Q res .Panels (e) and (f) illustrate the 10 m wind speed and MLD.The climatological values of the MLD and other variables with a 90-day high-pass filter applied are presented.A thick solid line indicates data points significant at the 95% level, whereas a thin dashed line represents the others.Specifically, (a), (c), and (d) show data derived from OISST, ERA5, and GODAS data, while panels (b), (d), and (f) display data derived from NICOCO simulation data.