1 Introduction

At the lower boundary of the atmosphere, sea surface temperature (SST) plays a central role in air–sea interactions. While it has been long recognised that low-frequency SST variability can strongly affect large-scale atmospheric circulation (e.g., Bjerknes 1969; Hendon 2003; Zhang and Anderson 2003), an increasing number of studies have found that high-frequency SST variability (e.g., the diurnal cycle of SST) can affect climate variability on intraseasonal to interannual timescales (e.g., Slingo et al. 2003; Bernie et al. 2005, 2007, 2008; Woolnough et al. 2007; Terray et al. 2012; Peatman et al. 2013; Ham et al. 2014; Birch et al. 2016; Tian et al. 2017, 2019).

The diurnal cycle of SST is usually small where incident heat is mixed over the first few metres to tens of metres of the ocean. However, in certain circumstances, in particular when surface winds are weak, a ‘warm layer’ can form during the day that can lead to diurnal variations varying from 0.2 to 3 K under different conditions (Kawai and Wada 2007 and references within). During calm and clear days, the sea surface tends to absorb more incoming shortwave radiation within the upper 1 m and forms a strong diurnal thermocline. During windy days, strong turbulence in the upper-ocean mixing layer can prevent the thermal stratification near the surface. In the meantime, the turbulence in the lower atmosphere draws energy from the ocean, leading to decreased diurnal amplitude of SST (Kawai and Wada 2007).

Previous observational studies have shown that a strong diurnal cycle in SST can play an important role in triggering afternoon convection over the western Pacific ocean (e.g., Chen and Houze 1997; Sui et al. 1997; Bellenger et al. 2010; Ruppert 2016; Ruppert and Johnson 2016), indicating that resolving the diurnal cycle of SST may be an important ingredient in reducing the biases often inherent in daily-scale simulated rainfall and convection in climate models.

Several modelling studies have quantified the impacts of sub-daily SST variation on large-scale variability by either changing the coupling frequency in coupled models or prescribing diurnal-varying SST in atmosphere models (e.g., Slingo et al. 2003; Bernie et al. 2005; Woolnough et al. 2007; Masson et al. 2012; Terray et al. 2012; Seo et al. 2014). Terray et al. (2012), for example, examined the influence of SST coupling frequency on the teleconnections between the Indian monsoon, El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). By running coupled general circulation model (GCM) simulations with different SST coupling frequencies, they showed that high-frequent exchange of SST (i.e. 2-hourly) led to an improved simulation of ENSO and the lead-lag relationship between the Indian monsoon and ENSO. They also found that the monsoon-IOD teleconnection is sensitive to SST coupling frequencies. Masson et al. (2012) found that decreasing SST coupling frequency from 2- to 24-hourly in a coupled model led to a systematic decrease in the amplitude (~ 15%) of ENSO. By using a one-dimensional ocean mixed layer model coupled to an atmosphere model, Bernie et al. (2005) found that including the diurnal cycle of SST can increase the intraseasonal variability of daily mean SST associated with the Madden–Julian Oscillation (MJO) in the western Pacific warm pool. They found that a realistic simulation of diurnal and intraseasonal SST variability requires at least a 3-hourly exchange of information between the atmosphere and ocean models and a high vertical resolution (at least about 1 m) in the uppermost ocean to resolve warm-layer processes.

The Maritime Continent is situated between the tropical Indian and Pacific oceans and within the western tropical warm pool. The climatic rainfall variability in this region is sensitive to SST variability in the surrounding tropical oceans (Aldrian and Susanto 2003). In addition, the Maritime Continent consists of numerous islands with complex topography that are surrounded by shallow waters, which is prone to intense atmospheric convection and heavy precipitation. The massive amounts of latent heat released from precipitation contributes to the rising branch of the Walker and Hadley circulations, subsequently influencing the global climate. Besides, this region is characterised by multi-scale interactions between the diurnal cycle and other large-scale low-frequency variability (e.g., Moron et al. 2010; Qian et al. 2010, 2013; Rauniyar and Walsh 2011, 2013; Oh et al. 2012; Birch et al. 2016). Given the importance of climate over the Maritime Continent to global climate, improved representation on the current climate over this region can provide confidence in model prediction on future projection (Chandrasa and Montenegro 2019). Due to the presence of complex topography and land-sea distribution in the Maritime Continent, it remains a great challenge to correctly simulate the weather and climate over this region. Increasing modelling studies have attempted to reduce the biases of precipitation by increasing model’s spatial resolution (e.g. Aldrian et al. 2004; Bhatt et al. 2016; Li et al. 2017), while some other studies also mentioned the importance of air-sea interaction (e.g. Aldrian et al. 2005; Bellenger et al. 2010; Wei et al. 2014; Xue et al. 2014).

Air-sea interactions in this region are complex because of the influence of local circulations generated by land-sea thermal contrast which dominate the local energy and hydrological cycles (Neale and Slingo 2003). Yang and Slingo (2001) showed that the diurnal cycle in rainfall over islands and surrounding seas is largely driven by a thermodynamical response to solar radiation with modulation from some local mesoscale processes. In coastal regions, land-sea breezes play an important role in the diurnal cycle, driven by a varying thermal contrast between land and sea. At times and locations where the SST diurnal cycle is large (e.g. when winds are weak), it is possible that this could modulate the timing and amplitude of thermal contrasts, thereby influencing land-sea breezes and diurnal convection. Moreover, Seo et al. (2014) suggested that changes in the mean SST and latent heat flux caused by the SST diurnal cycle can modify atmospheric convection in the Indian Ocean. Such a mechanism might also play a role in affecting diurnal convection and rainfall over the Maritime Continent region.

A set of coupled and uncoupled modelling experiments conducted by Xue et al. (2014) revealed the influence of the diurnal cycle of SST on air-sea interactions over the shallow water region of the Maritime Continent through a negative feedback mechanism. They found that coastal SST perturbations are more quickly dissipated in a coupled simulation with a 6-hourly SST coupling frequency compared to daily or weekly coupling frequency, as enhanced latent heat and moisture fluxes facilitate the development of low-level clouds that shield the water from incoming solar radiation. Their study primarily focused on the impacts of air-sea interaction in modulating SST variation and suggested that a high SST coupling frequency is necessary to reproduce realistic air-sea interaction in the Maritime Continent shallow water region. However, very few studies have attempted to investigate the effects of fast air-sea interaction on mean and diurnal cycle of precipitation over the Maritime Continent. In this paper, we examine the effect of coupling frequency on mean state and diurnal variations of rainfall and other properties over the Maritime Continent using a regional coupled ocean–atmosphere model. This paper is organised as follows. In Sect. 2 the model and experiments are described. In Sect. 3 the diurnal cycle of SST in the model is evaluated against observations, and differences in the mean state and diurnal cycles with different coupling frequencies are examined, and possible mechanisms are explored. Further discussion and conclusion are presented in Sect. 4.

2 Data and methodology

2.1 Model

We utilise the NEMO-OASIS-WRF coupled regional model (NOW, Samson et al. 2014) and apply it to the Maritime Continent region (d02 in Fig. 1) with a horizontal resolution of 1/12° for both atmospheric and oceanic components. Such resolution is sufficient to simulate the main topographic structures, but not to explicitly resolve convection. To have a smooth transition between the coarse boundary conditions and our 1/12° domain, this high-resolution simulation is two-way nested within a larger domain (d01 in Fig. 1) operating at 1/4° resolution in both the ocean and atmosphere. The oceanic and atmospheric components use a common horizontal resolution and are coupled through the OASIS3-MCT2 coupler (Valcke 2013) and the exchanged fields between the ocean and atmosphere include SST, ocean currents, wind stress, longwave and shortwave radiations, turbulent heat fluxes, precipitation and evaporation.

Fig. 1
figure 1

Observational June to October mean of SST averaged from 2006 to 2009 in the domain (d01, 30°S–30°N and 70°E–180°E). The nested domain (d02, 20°S–20°N and 90°E–160°E) is indicated within the dashed box. The observational SST data is the daily optimum interpolation SST from NOAA AVHRR (Advanced Very High Resolution Radiometer, Reynolds et al. 2007). SPO and SIO mark the mooring sites in the Pacific (8°N, 137°E) and Indian Ocean (5°S, 95°E) used to derive observed SST time series

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The oceanic component of NOW is the Nucleus for European Modelling of Ocean model (NEMOv3.4, Madec 2008). To better capture processes important for a realistic SST diurnal cycle, NEMO is configured with 75 vertical levels, with thicknesses from 1 m at the surface to 200 m at depth. This surface resolution has been shown to be sufficiently high to resolve the structure of the upper ocean and, in particular, the surface warm layer that can undergo large diurnal temperature variations (Bernie et al. 2005, 2007; Masson et al. 2012). NEMO is run with a prognostic turbulent kinetic energy scheme for vertical mixing, a Laplacian operator for isoneutral diffusion of tracers and a bi-Laplacian operator for lateral diffusion of momentum. Our configuration does not resolve tides, but includes a special treatment of tidal mixing to account for the dissipation of internal tides that are important in the deep narrow straits of the Indonesian Throughflow region (Koch-Larrouy et al. 2010). Vertical penetration of solar radiation in the ocean (in the visible spectrum) is applied through a three-waveband scheme (Lengaigne et al. 2009) that depends on the climatological seasonal chlorophyll-A concentration from the SeaWIFS dataset (O’Reilly et al. 1998). The open boundary conditions of NEMO are prescribed from a global ocean simulation at 0.25° resolution with 75 levels, namely, ORCA025-L75-MJM95, provided by the DRAKKAR/MyOcean group (The Drakkar group 2007). ORCA025-L75-MJM95 was forced by the 3-hourly ERA-interim atmospheric reanalysis (Dee et al. 2011) through the CORE bulk formulae, with a correction of radiative fluxes, sea surface salinity relaxation, and restoring for a few overflows and bottom waters (Barnier et al. 2011). The initial conditions for ocean temperature and salinity is from Levitus98 (Levitus et al. 1998) with an ocean at rest (u = 0 and v = 0).

The atmospheric component of NOW is the Weather Research and Forecasting model (WRFv3.6, Skamarock et al. 2008) with the Advanced Research WRF (ARW) dynamic core. WRF uses a terrain-following hydrostatic pressure coordinate with 45 vertical levels. The atmospheric model is based on a simple diffusion, non-hydrostatic model with gravity wave drag (Shin et al. 2010) and smoothed topography. Convection processes are parameterized using the Grell-3D cumulus convective scheme, which uses an ensemble (effectively 144 members) of triggers and closures with varying parameters under different initial conditions and takes the mean of the ensemble to feed back to the model (Grell and Dévényi 2002). Other WRF physical parameterization used in this study include the WRF single-moment 6-class microphysics scheme (WSM6, Hong and Lim 2006), the Rapid Radiative Transfer Model (RRTM) longwave scheme (Mlawer et al. 1997), the Goddard two-stream multi-band shortwave scheme (Chou and Suarez 1999), unified Noah land-surface model (Tewari et al. 2004), and Yonsei University planetary boundary layer scheme (Hong et al. 2006). WRF lateral boundary conditions are relaxed towards the European Centre for Medium Range Weather Forecasts (ECMWF) ERA-Interim 0.75° resolution reanalysis at 6-hourly intervals (Dee et al. 2011). Initial conditions for the atmosphere are from the ERA-Interim reanalysis on the 1st of January 1989.

The coupled model configuration is identical to the highest horizontal resolution simulation described in Li et al. (2017), which showed reasonable representation of large-scale SST and rainfall. The magnitude of rainfall diurnal cycle over the domain is also reasonably represented, although in common with other coupled models, the daily maximum rainfall over land arrives 2–3 h earlier than observation (Li et al. 2017).

2.2 Experiments

To quantify the effect of coupling frequency on the mean rainfall and its variability, two coupled NOW experiments with different ocean–atmosphere coupling frequencies are conducted. In the first experiment (hereafter NOW1h simulation), WRF and NEMO exchange information every hour via the OASIS3-MCT2 coupler, while in the second experiment the coupling frequency is reduced from 1 to 24 hourly (hereafter NOW24h simulation) such that daily averaged quantities are passed between ocean and atmosphere. Both NOW1h and NOW24h simulations are run for 5 years 2005–2009. In addition to the coupled simulations, a complementary WRF-only experiment was conducted to isolate the effect of different SST mean states found between NOW1h and NOW24h coupled experiments. This WRF-only simulation is forced by daily-mean SST calculated from the NOW1h simulation, hereafter WRF24h, and also run from 2005 to 2009. The atmospheric lateral boundary conditions in WRF24h are identical with the coupled runs. We found that there is a substantial drop in domain-averaged SST during the first month in the year 2005 for NOW24h (not shown). This is an adjustment from initialization using different coupling frequencies, instead of drift. We have discarded the whole year of 2005 to ensure that our results are not affected by drop and that the model’s upper ocean is stabilized (Table 1).

Table 1 Description of all experiments
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2.3 Observational datasets

There is limited high temporal frequency SST data available for the Maritime Continent region. To evaluate the SST diurnal cycle in our simulations, we utilise high temporal resolution in-situ temperature data at 1 m depth derived from a TAO/TRITON mooring in the Pacific Ocean and a RAMA mooring in the Indian Ocean (McPhaden et al. 2010). SST from these moorings is available at least every hour and available for more than 85% of days during the period from 2006 to 2009. The locations of these moorings are shown in Fig. 1. The observational SST is the NOAA high-resolution daily SST version 2, blended from in situ data and infrared satellite data from the Advanced Very High Resolution Radiometer (AVHRR) using optimum interpolation (AVHRR-OISSTv2, Reynolds et al. 2007). The AVHRR-OISST is available from 1985 to present day on a 0.25° × 0.25° global grid. The observational precipitation data used in this paper are from Tropical Rainfall Measuring Mission (TRMM, Huffman et al. 2007). We use TRMM monthly 3B43v7 and 3-hly 3B42v7, available from 1998 to present day with a 0.25° × 0.25° spatial grid, to evaluate the simulated precipitation climatology and diurnal cycles. The observational sea surface wind used in this study is QuikSCAT 10-m wind estimate which is retrieved from NASA’s Quick Scatterometer that operatred from June 1990 to November 2009 (QuickSCAT, Lungu et al. 2006).

3 Results

3.1 Evaluation of the simulated SST diurnal cycle

Figure 2a, b shows the mean diurnal ranges of SST from the NOW1h simulation for two broadly defined seasons: Asian summer monsoon season (June–October, JJASO) and Australian summer monsoon season (December–April, DJFMA). The diurnal range is defined as daily maximum SST minus daily minimum SST. In the simulation, the magnitude of the SST diurnal range varies with seasons: a belt with large SST diurnal range (> 0.4 °C) swings between south and north of the equator responding to the seasonality of insolation. In addition, relatively large SST diurnal ranges (> 0.8 °C) are found near some coasts, which suggests the modulation from coastal processes.

Fig. 2
figure 2

a Diurnal SST range derived from NOW1h simulation averaged from JJASO season during the period of 2006–2009. b As in a, but from DJFMA. In a, the two red dots show the mooring sites in the Indian Ocean (SIO: 5°S, 95°S) and the Pacific Ocean (SPO: 8°N, 137°E). e 31-day running mean of SSTs derived from the locations of SIO and SPO moorings (see a) for the NOW1h simulation and observations at 1 m depth. d Seasonally averaged diurnal cycles of SST from the model and observation at the SIO mooring location against Coordinated Universal Time (UTC) and local solar time (LST). e As in d, but for the SPO location

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The simulated 2006–2009 daily SST time-series and the diurnal cycle of SST from NOW1h are evaluated at the locations of the TAO/TRITON moorings: SIO and SPO (Fig. 2). The SST from the NOW1h simulation is too cold (warm) at SIO (SPO) by ~ 1 °C (Fig. 2c). The correlations between daily SST time-series of observation and simulation are 0.51 and 0.45 for SIO and SPO, respectively, which indicates that about 25% of the SST variance can be explained by the forcing signal at the boundary. Such moderate correlations may be partly due to intrinsic variability in the oceanic (Penduff et al. 2011) and atmospheric (Jourdain et al. 2011) components.

At the SIO site, the observed seasonally-averaged SST diurnal cycles show a SST peak at ~ 1500 local solar time (LST) for all seasons, with maximum SST diurnal range (~ 0.40 °C) in DJFMA and reduced diurnal range (~ 0.16 °C) in JJASO (Fig. 2d). Compared to observation, the daily peak in simulated SST is delayed by ~ 2 h, occurring at about 1700 LST in both seasons (Fig. 2d). The SST diurnal ranges in the NOW1h simulation show comparable magnitude in DJFMA to observations whereas they are overestimated in JJASO by up to ~ 0.1 °C. Similar to the SIO site, the SST diurnal cycles at SPO show a 2-h delay of daily maximum SST in the NOW1h simulation compared to observation (Fig. 2e). In addition, the SST diurnal ranges in the simulation are slightly overestimated in both seasons at this location.

Due to scarce high-frequency SST observations in this region, the comparisons between the model and observation are only based on these two moorings. In general, the simulation shows diurnal ranges at these locations that are too large and delayed by about 2 h. There are clear biases in both the mean state and diurnal cycle in the model. As such our results need to be interpreted with these in mind. While it is clear that there are some errors in the representation of sub-daily SSTs, the coupled model is able to represent the overall seasonality and the amplitude/timing of SSTs.

3.2 Effects of coupling frequency on mean state

In the NOW24h simulation, annual mean SST is considerably warmer than NOW1h over the Southeast Indian Ocean off Java and Sumatra, with the largest difference (> 0.5 °C) in the vicinity of southwest of Sumatra (Fig. 3a). In contrast, the eastern part of domain and northeast of Sumatra in NOW24h show significantly (p < 0.05) cooler annual mean SST by ~ 0.2 °C than NOW1h. The difference in surface wind is consistent with these SST changes (i.e., more surface convergence towards warmer areas). Additionally, broad scale north-easterly anomalies over the Maritime Continent are consistent with a cooler Pacific and warmer south Indian Ocean (Fig. 3a). Examining these changes by month, it is clear that the differences do not occur in all months but are restricted to the South Asian monsoon season (i.e., from June to October, JJASO). The magnitude of mean SST changes averaged from all JJASO seasons exceed 1 °C to the southwest of Sumatra (Fig. 3a-I), whereas there is no significant change in SST over the remaining months (Fig. 3a-II).

Fig. 3
figure 3

a Differences in mean SST and 10 m-wind velocity between NOW24h and NOW1h simulations (i.e. NOW24h-NOW1h) for the period of 2006–2009. Also shown are the corresponding SST and wind differences averaged over JJASO (a-I) and over the remaining months (a-II). b As in a, but for precipitation. The significant differences (at the 0.05 level based on two tailed Student’s t test) are stippled

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Mean annual precipitation shows significant changes over the north of New Guinea islands and west of Sumatra (Fig. 3b). Over the north of New Guinea, the SST change is not significant (Fig. 3a) while a significant decrease of precipitation is found (Fig. 3b). The significant decreased precipitation may be driven by decreased low-level convergence (see Suppl. Fig. 2). In Fig. 3b, significantly reduced annual mean precipitation is found around 5°N from the equatorial eastern Indian Ocean to northern Sumatra in NOW24h compared to NOW1h, whereas increased precipitation tends to occur over the ocean west of Sumatra between the equator and 5°S in NOW24h. These differences in annual mean precipitation are again only found during the South Asian summer monsoon season (i.e., JJASO), when the large changes in SST occur. During JJASO, the mean difference over the dashed box exceeds 5 mm·day−1 on average (Fig. 3b-I).

Differences in SST in JJASO between NOW24h and NOW1h are having an influence on winds and precipitation. To test whether the changes in precipitation are purely due to differences in the mean state of SST or whether high frequency coupling is playing a role, we examine the atmosphere-only WRF24h experiment that is forced by daily-mean SST derived from NOW1h. As such, the lower atmosphere in WRF24h interacts with the same SST daily mean but does not see the diurnal changes simulated in NOW1h. Both during JJASO and the remaining months, the differences in precipitation between WRF24h and NOW1h are much smaller than the difference between NOW24h and NOW1h during JJASO, and not statistically significant (see Suppl. Fig. 3). This suggests that the main precipitation differences between the coupled simulations are primarily due to a change in the mean SST rather than that in the diurnal variability of SST or to the wind-current feedback (Renault et al. 2016) which are both present in NOW1h but not in WRF24h.

Given that significant differences in mean state SST and precipitation are only found off the southwest coastal area of Sumatra in JJASO, the remainder of the analysis focuses on this region during the South Asian monsoon season.

3.3 Wind-thermocline-SST feedback

The difference of monthly averaged net surface heat fluxes between NOW1h and NOW24h were firstly examined in the area where the significant change in SST occurs, which shows a damping effect of net surface heat flux on SST signal (not shown). Then, the question which arises, is how the warmer SST in NOW24h is maintained off southwest Sumatra. The Java-Sumatra coast is characterised by offshore Ekman transport and consequently strong upwelling generated by the southeast monsoon winds during JJASO. This produces a seasonal cooling (Susanto et al. 2001). This cooling is reproduced in the coupled simulations (see Suppl. Fig. 4). In addition, the low SST shows north-westward migration along the Java-Sumatra coast during JJASO, which is consistent with Susanto et al. (2001). As noted above, the mean SST southwest of Sumatra and averaged over JJASO is ~ 1 °C warmer in NOW24h than in NOW1h (Fig. 3a-I).

Given that this is occurring during the South Asian monsoon (JJASO) when winds are at their strongest, it would seem feasible that the differences in SST may be related to differences in the rate of upwelling along the southwest coast of Sumatra. We first examine the mean vertical velocity averaged over the Sumatra region where significant SST difference occurs. Both simulations show a similar seasonal cycle of vertical velocity with strong upwelling during JJASO which peaks in July and August (~ 1.5 m·day−1) at ~ 50 m depth in both simulations (see Suppl. Fig 5). However, the differences in vertical velocity between two coupled simulations during JJASO are not significant. As such changes in Ekman pumping velocities are unable to explain the differences in SST between these two simulations and other processes must be important.

Figure 4 shows the depth of 20 °C isotherm (which can be used as a proxy for the depth of the thermocline) and the averaged surface zonal wind stress along the eastern equatorial Indian Ocean. In the NOW1h simulation, we can see that the thermocline depth gradually becomes shallower southeastwards along the southwest coast of Sumatra during JJASO (Fig. 4a). This pattern is consistent with wave adjustment due to the seasonal wind reversal along the equator (Fig. 4d). The change in seasonal equatorial easterly wind leads to an Ekman divergence that shoals the thermocline along the equator generating an eastward propagating equatorial Kelvin wave (Schott et al. 2009). On reaching the Sumatran coast, this continues polewards as a coastally trapped Kelvin wave. In Fig. 4a, the wedge pattern of thermocline depression is suggestive of the subsequent westward propagation of Rossby waves that propagate the signal offshore (Yu et al. 2005). Figure 4d shows that there is a less distinct seasonal reversal in the winds from westerly to easterly along equatorial Indian Ocean during JJASO in NOW24h compared to NOW1h. Especially, the reversal of equatorial winds at the start of the monsoon season completely fails in 2007 in the NOW24h simulation. The weaker easterlies in NOW24h would weaken the effect of the seasonal uplift of the thermocline by the propagation of equatorial and coastal Kelvin waves, which leads to a deeper thermocline (Fig. 4b). The deepened thermocline caused by weaker easterlies in NOW24h is significant at the level of 5% (Fig. 4b), and the significance remains even after removing the year 2007 when the easterlies completely reverse to westerlies (not shown). In addition, the deepened thermocline along the coast of Sumatra in NOW24h almost occurs in JJASO of every year during the period of 2006–2009 (Fig. 4c), and a strong correlation (r = 0.68) can be found between thermocline depth and SST off Sumatra in their pentad timeseries. This robustly suggests that a deeper thermocline would make it harder to bring cool deep water to the surface via the normal seasonal upwelling and this would ultimately lead to the relatively warmer seasonal SST in NOW24h. As demonstrated by the comparison between NOW1h and NOW24h experiments, the increase in mean SST leads to anomalous northwesterlies and thus even weaker seasonal easterlies along the equator. As such there appears to be a positive wind-thermocline-SST feedback mechanism that maintains the relatively warm SST to the southwest of Sumatra.

Fig. 4
figure 4

The 20 °C isotherm (Z20) depth averaged over all JJASO during period 2006–2009 for a NOW1h and b NOW24h–NOW1h. Stippling areas in b show statistically significant differences (p < 0.05). The timeseries of c Z20 depth averaged over the Sumatra area where difference of mean SST exceeds 1 °C during JJASO and d surface zonal wind stress averaged along equator from 91°E to 100°E (ocean only) for two simulations and their difference. The positive and negative in d indicates westerly and easterly, respectively

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3.4 Precipitation-barrier layer-SST feedback

Du et al. (2005) showed that seasonal SST variation off Sumatra is also influenced by the barrier layer thickness (BLT). The barrier layer is an intermediate layer between the base of the mixed layer (determined by density) and the top of the thermocline (Godfrey and Lindstrom 1989; Du et al. 2005). A thick barrier layer can occur in regions where stable stratification forms because of large freshwater input. A barrier layer impedes heat exchange between the colder sub-thermocline waters and the surface. The NEMO model diagnoses the BLT as the difference between top of thermocline depth (i.e. the depth above which the temperature is greater than the surface temperature at 10 m depth minus 0.2 °C) and pycnocline depth (i.e. the mixed layer depth in density with a variable threshold criterion equivalent to a 0.2 °C decrease).

We focus on the region, near the southwest of Sumatra, where both SST and precipitation are enhanced in NOW24 during JJASO (boxed region in Fig. 5b, right panel). In that region, the mean SST starts to decrease in June every year and reaches a minimum in August–September for both NOW simulations (Fig. 5a). The seasonal surface cooling is associated with strong coastal upwelling induced by strong monsoonal south-easterlies, which can be reinforced by positive wind-evaporation-SST feedback (Susanto et al. 2001; Du et al. 2012). This sea surface cooling during the monsoon season is weakened in NOW24h compared to NOW1h in all years (although the difference is weak in 2009), suggesting that this is a robust seasonal difference between these two simulations.

Fig. 5
figure 5

Left panels show the time series of a daily SST averaged from the Sumatra area where difference of mean SST exceeds 1 °C during JJASO, b 31-day running mean of precipitation averaged from dashed box (91.5°E–99.5°E, 4°S–1°N) shown in corresponding right panel, and c 31-day running mean of BLT averaged from dashed box (91.5°E–99.5°E, 4°S–1°N) shown in corresponding right panel. Here are shown NOW1h (blue), NOW24h (red) and the NOW24h-NOW1h difference (dark blue bars). The grey stripes in left panels indicate the time span from June to October. Right panels show the composites NOW24h-NOW1h difference averaged from JJASO for a SST, b precipitation and c BLT. Stippling areas in right panels show statistically significant differences (p < 0.05)

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At the same time, stronger mean JJASO precipitation near the southwest coast of Sumatra is also found for all years in NOW24h during JJASO compared to NOW1h (Fig. 5b). This is likely related to increased latent heat fluxes as a result of warmer SST in NOW24h. Increased precipitation leads to greater freshwater input to the ocean surface, which results in a thicker BLT. Indeed, the precipitation and BLT anomalies are clearly co-located (right panel of Fig. 5c). Although there are differences between the simulations in BLT for all seasons, in all years the BLT is thicker in NOW24h, particularly during the second half of the monsoon (Fig. 5c).

This suggests that a local precipitation-barrier layer-SST positive feedback may also contribute to the difference between NOW24h and NOW1h. Greater precipitation over the region of warmer SST and increased wind convergence contributes to a thicker barrier layer that in turn maintains warmer SST by suppressing the entrainment of cold sub-thermocline water at a time when upwelling is strong.

3.5 Diurnal cycle of precipitation and wind over Sumatra

We have shown that mean SST and precipitation southwest of Sumatra during JJASO depend on model coupling frequency. In this section, we investigate the impact of coupling frequency on the diurnal cycle of precipitation during JJASO. To remove the effect of mean differences between the simulations, these analyses are based on the diurnal departure from their daily means. For NOW1h, the onshore propagation of rainfall starts from 1000 to 1300 LST along the southwest coast of Sumatra (Fig. 6, top row), reaching peak rainfall (~ 10–15 mm·day−1) over the northwestern part of the island and southwest coast over the next three hours (1300–1600 LST). Compared to the TRMM-3B42, the peaking time is ~ 3 h earlier (As-syakur et al. 2019). Offshore propagation starts along the northeast coast from ~ 1900 to 2200 LST and maximum rainfall over the surrounding sea occurs in the early morning ~ 0400–0700 LST.

Fig. 6
figure 6

Composites of diurnal precipitation for a 0000 to 1200 and b 1200 to 2400 UTC relative to the mean daily precipitation during JJASO. Both UTC and LST are shown. Shown are the diurnal anomalies of precipitation at each time for NOW1h (top row), NOW24h-NOW1h (middle row) and WRF24h-NOW1h (bottom row)

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The largest diurnal precipitation range (> 25 mm·day−1) over land occurs over northern and coastal southwest Sumatra, whereas the largest diurnal cycle of oceanic rainfall occurs near the northwest and northeast coastal sea in NOW1h simulation. This also corresponds to the regions that exhibit the largest differences (> 3 mm·day−1) between NOW24h and NOW1h.

To examine these regions in more detail, we calculate the averaged diurnal cycle over the areas shown in Fig. 7a, b (see caption for criteria used to define these regions). For the northern land region (NLand; Fig. 7c), peak rainfall and minimum rainfall during JJASO occur at ~ 1400 LST and ~ 0800 LST, respectively, for both the NOW1h and WRF24h simulations. In contrast, NOW24h shows a substantial decrease of peak rainfall by ~ 8 mm·day−1 with about an hour delay in peak timing and a slight increase of minimum rainfall by ~ 3 mm·day−1, which results in reduced diurnal cycle (by ~ 11 mm·day−1 in range). Similarly, the NOcean region (Fig. 7e) has a weakened diurnal cycle in NOW24h with a ~ 12 mm·day−1 reduction in range from ~ 30 mm·day−1. Conversely, over the southern land (SLand) and southern ocean (SOcean) regions there are substantial increases in the JJASO diurnal ranges by ~ 12 mm·day−1 and ~ 7 mm·day−1, respectively (Fig. 7d, f). Compared to NOW1h and WRF24h, there is also ~ 1 h delay in peak precipitation over SLand region for NOW24h. No significant change in the diurnal cycle is found outside of the monsoon season, or in other regions.

Fig. 7
figure 7

a, b The northern and southern regions of Sumatra highlighting the areas with large differences in the diurnal cycle of precipitation (colour-shaded). Diurnal cycles of precipitation anomalies averaged over selected regions of c north land (NLand, yellow patch in a), d south land (SLand, green patch in b), e north ocean (NOcean, pink patch in a), and f south ocean (SOcean, blue patch in b). The selection criteria for the area are the JJASO absolute difference of peak diurnal precipitation between NOW24h and NOW1h exceeds 3.5 mm·day−1 for the NLand, NOcean and SLand regime, and exceeds 2.5 mm·day−1 for the SOcean regime. Solid lines are the averages from JJASO whereas dashed lines are the averages from the months outside of JJASO

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In summary, we see a large change in diurnal rainfall amplitude and up to 1-h delay in peak diurnal rainfall between NOW24h and NOW1h. However, the similarity between NOW1h and WRF24h (which have identical mean SST) demonstrates that these diurnal cycle changes come about because of differences in the mean state and not as a direct result of the SST diurnal cycle (e.g., from changes in the timing or amplitude of the land-sea temperature gradient).

To investigate whether the changes in diurnal rainfall are caused by the changes in moisture convergence associated with land-sea breezes, we examined the vertical profiles of moisture convergence/divergence and wind anomalies along sections perpendicular to the coastlines for the northwestern and southwestern Sumatran regions (Fig. 8). The typical low-level land-sea breeze circulations are evident over both northwestern and southwestern coast in NOW1h (Fig. 8a, c). The sea breeze starts from ~ 1000 LST, developing and reaching its maximum (> 0.4 m·s−1 in speed) in the afternoon, with a strong accompanying return flow (> 0.2 m·s−1 in speed) aloft at ~ 800 hPa. The sea breeze reverses to land breeze from ~ 1900 LST and persists until morning (before ~ 1000 LST). Compared to the sea breeze circulation, the land breeze cell is much weaker. The strong low-level (below 900 hPa) moisture convergence (> 1.5 g·kg−1·day−1) co-occurs with the onset of onshore wind from ~ 1000 LST, with divergence aloft occurring between ~ 850 and 750 hPa. This convergence decays at ~ 1600 LST and, in the meantime, strong convergence occurs at ~ 850 hPa. This strong convergence aloft leads to the sinking of air that causes the divergence at surface in the afternoon. For NOW1h, the land-sea breeze circulations over northwestern coast (Fig. 8a) are much stronger than southwestern coast (Fig. 8c). This is consistent with the larger rainfall diurnal cycle of rainfall over northwestern coast compared to the southwestern coast (Fig. 7) in the NOW1h simulation.

Fig. 8
figure 8

a, c Vertical profiles of the diurnal cycle of moisture convergence/divergence (shaded) and wind (contour) anomalies perpendicular to the coast and averaged along the Northwestern and Southwestern Sumatran coastline in Fig. 7a and b for NOW1h during JJASO, respectively. b, d Show the differences of diurnal cycle of moisture convergence/divergence and wind between NOW24h and NOW1h. Red (blue) shades represent onshore moisture convergence (divergence). Solid (dashed) lines represent onshore (offshore) wind. For wind anomaly, the grey thick lines denote 0 m·s−1 and contour interval (CI) is shown in each panel

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Over the northwestern coast, NOW24h shows little changes on the surface convergence and divergence aloft at ~ 1300 LST compared to NOW1h. There are no substantial changes in the surface onshore wind in NOW24h. Onshore wind decreases and reverses to offshore with height from surface to upper atmosphere, reaching a maximum at ~ 800 hPa with increases of ~ 0.08 m·s−1 in speed (Fig. 8b). This indicates a weakened land-sea breeze circulation in NOW24h compared to NOW1h, which may explain the decreased amplitude of the rainfall diurnal cycle in NOW24h over this region (Fig. 7c, e). In contrast, the surface convergence (divergence aloft) at ~ 1300 LST is stronger in NOW24h, which is consistent with the stronger surface onshore wind (offshore wind aloft) in NOW24h over southwestern coast (Fig. 8d). The enhanced land-sea breeze in NOW24h can explain the amplified diurnal cycle of rainfall over northwesterrn Sumatra (Fig. 7d, f). However, it remains unknown whether the weakened land-sea breeze circulations over northwestern coast in the afternoon during the South Asian monsoon season is directly linked to the decreased mean SST in the vicinity of western Sumatra in the NOW24h simulation. Similar question also needs to be addressed for the southwestern coast.

4 Discussion and conclusion

This study investigates the effects of coupling frequency on the mean state and diurnal variation of SST and precipitation over the Maritime Continent region by comparing two coupled simulations with identical configuration but 1- and 24-hourly coupling frequency for all exchanged fields. Two areas with significant changes of precipitation are found, that is, the north of New Guinea and west of Sumatra. Only the west of Sumatra also shows significant changes of SST. The significant changes of SST and precipitation are primarily found near the western coastal area of Sumatra and its surrounding sea during the South Asian monsoon season, a period and region that is typically associated with strong air-sea feedback (Du et al. 2005). Compared to observation (Suppl. Fig. 1a), the seasonal mean SST during the South Asian monsoon season shows cold biases (~ 2 °C) in the same area where the significant change of SST is found for the simulation with 1-hrly coupling frequency. In the meantime, NOW1h shows a strong easterly bias along the equator in tropical Pacific flanked by a westerly bias north off equator (Suppl. Fig. 1a). For precipitation in the South Asian monsoon, the dry biases are found along the belt between equator and 5°S and eastern rim of the north Indian Ocean whereas wet biases are widespread over the northern part of the domain in NOW1h (Suppl. Fig. 1c). Compared to NOW1h, NOW24h shows similar biases pattern but with reduced magnitude in biases for some areas, such as western Pacific and southwest of Sumatra (Suppl. Fig. 1b and d). Based on the evaluation on seasonal mean SST and precipitation, it is not able to conclude that the simulation with 1-hrly coupling frequency is more realistic. However, this can suggest that some local processes (e.g. at southwest of Sumatra and western Pacific warm pool) are prone to the changes in coupling frequency.

Figure 9 summarises the possible mechanisms that explain the monsoon season changes in the lower atmosphere and ocean surface when the coupling frequency is damped. Two potential feedbacks are identified that contribute to the maintenance of warmer SST near the southwest of Sumatra: (1) a remotely driven positive wind-thermocline-SST feedback (red shaded in Fig. 9b) and (2) a local positive precipitation-barrier layer-SST feedback (blue shaded in Fig. 9b). These two feedbacks can only occur during the South Asian monsoon season.

Fig. 9
figure 9

a Schematic of the possible mechanisms for NOW24h relative to NOW1h (i.e. when reducing coupling frequency) and b Flow diagram of the processes occurring during the South Asian monsoon season with highlights on two positive feedback loops: (1) large-scale wind-thermocline-SST positive feedback (shaded in orange) and (2) local precipitation-barrier layer-SST positive feedback (shaded in blue). In a and b, the processes that coupling frequency (CF) has little effects are in red, whereas processes in black are the changes when reducing CF from 1- to 24-hourly

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During the South Asian monsoon, the tropical eastern Indian Ocean is affected by strong south-easterlies, which prevail along the southwest coast of Sumatra. Such sustained southeasterly winds lead to offshore transport in the surface ocean layer and result in upward transport of colder waters. The coastal upwelling and offshore transport are well simulated in both simulations. While the SST along the southwest coast off Sumatra is much warmer (> 1 °C) without diurnally varying air-sea interactions, there is no significant difference in the upwelling rates in this region between the two simulations. Instead, in the simulation with the damped coupling frequency, the normal seasonal reversal of the eastern Indian Ocean equatorial trade winds to an easterly direction at the start of the monsoon season is suppressed. The resultant anomalous equatorial westerlies in the daily-coupled simulation leads to upwelling Kelvin waves that propagates from the equator southwards along the Sumatran coast, deepening the thermocline relative to the hourly-coupled experiment. Despite little overall difference in the vertical velocity, the deeper thermocline means that upwelled water is warmer, and there is less entrainment in west of Sumatra. The warmer SST in the eastern Indian Ocean is in turn conducive to a further enhancement of the anomalous north westerlies (including the equatorial westerlies)—reinforcing the initial response.

A second factor that enhances the mean SST in the daily-coupled simulation relates to the development of the seasonal barrier layer in the vicinity of the southwest of Sumatra. Several thermodynamic and dynamic processes are involved. Higher precipitation due to a thermodynamic response to the warmer SST (possibly triggered by the first large-scale mechanism) and a greater low-level moisture convergence during the South Asian monsoon season causes increased salinity stratification in the surface ocean, and a thicker barrier layer. This helps to maintain warmer SST by impeding the vertical mixing of cooler water into the mixed layer (Du et al. 2005). The warmer SST, in turn, releases more latent heat that triggers increased precipitation. The atmospheric response to warmer SST in the eastern Indian Ocean further contributes to the weakening of the equatorial easterlies. Thus, these large-scale and local positive feedbacks interact with each other through warmer SST. This precipitation-barrier layer-SST chain of events is similar to the feedback mechanism operating on interannual timescales associated with positive IOD events described by Du et al. (2012).

Comparison between our atmosphere-only simulation and hourly-coupled simulation that both have the same SST mean state shows no significant difference in mean precipitation in any months. This suggests that the mean differences in precipitation are primarily driven by differences in mean SST rather than from the inclusion of a diurnal cycle by themselves. Future targeted experiments are needed to understand how the changes in coupling frequency can affect the changes in mean state over this region.

Interestingly, the years of 2006–2008 were three consecutive strong positive IOD events where anomalously cold SST appeared in the eastern tropical Indian Ocean and the mechanisms described above are similar to the processes important for the development of IOD events (e.g., Cai et al. 2009a, b; Du et al. 2012). This may indicate the importance of coupling frequency in better simulating IOD events in addition to modulating the seasonal evolution of regional climate. The different background states for these three years may explain the weaker changes noted in the final year of our simulation (i.e., the year of 2009). Further work, and longer simulations are needed to understand the importance of coupling frequency on interannual timescales.

In addition to the mean precipitation, the diurnal cycle of precipitation over Sumatra is also sensitive to the coupling frequency. Although coupling frequency showed little effect on changes in the timing of peak precipitation (up to 1-h difference), it does significantly influence the amplitudes of the diurnal cycle. The 1-h delay of peak precipitation between NOW24h and NOW1h can be attributed to the difference in background westerlies over Sumatra, consistent with the findings from Mori et al. (2004) that show importance of the background westerlies to the land-sea breeze and propagation of precipitation diurnal cycle over the Sumatra Island. The amplitude of the diurnal cycle is reduced over the northern part of Sumatra whereas it is increased over the southwest coast of Sumatra when the coupling frequency is damped. The modified diurnal precipitation is associated with changes in land-sea breeze circulation. Comparison of our coupled and forced simulations again indicates that the changes in diurnal circulation and precipitation are not directly related to the inclusion of a diurnal cycle in SST that could for example modify the diurnal land sea temperature gradient through the day. Instead the modified diurnal precipitation may be related to the difference in the mean moisture availability over these two regions.

Many questions remain unanswered to thoroughly understand the mechanism. For example, why is it the western Maritime Continent that is sensitive to coupling frequency? What are the initial triggers of the seasonal changes, such as the suppression of the equatorial wind reversal during the South Asian monsoon season? There are some possible processes whereby the ocean may be modified by changes in atmospheric coupling. Firstly, the atmospheric circulations related to diurnal convection are not seen by the ocean in the experiment with daily coupling frequency. Moreover, moving storms/mesoscale convective systems are averaged over 24 h in the daily coupling frequency simulation, and are therefore no longer able to force inertial oscillations in the ocean (e.g., Price 1981, 1983). It would be useful to test whether the differences stem from the wind averaging. This could be examined in ocean-only simulations forced by 1- or 24-h averaged wind stress from the NOW1h simulation. More broadly, future investigations by carrying out experiments with varying coupling frequencies for atmospheric or oceanic variables separately can help to address the ultimate questions on cause-effect relationship between each variable.

Some questions may arise as to whether the results are robust if the western boundary of child domain (i.e. d02) is shifted westward given the possibly existed discontinuities along the d01/d02 boundary. In our study, the 2-way nesting was especially developed to avoid discontinuities (compared to 1-way nesting), and the physical parameterizations are the same in the parent and child domains. Even though, it is possible that some of the differences stem from numerical issues along the boundary. Ideally global simulations could address this question, however which is impractical at such spatial resolution. Nevertheless, future experiments could extend or shift the domain eastwards to see if our results remain robust.

In conclusion, our experiments demonstrate the importance of coupling frequency on both mean precipitation and the diurnal cycle of precipitation over Sumatra, where the coupling frequency does not appear to directly affect local precipitation, but influences the precipitation through a series of air-sea processes that lead to a change in mean state of SST. Our study suggests that for regional downscaling experiments (either coupled or atmosphere-only) resolving diurnal SST variations needs to be considered in some experiments as it can significantly affect conditions across a range of timescales in some regions and seasons.