3.1. MISO characteristics
An intra-seasonal signal is first obtained by applying a 20–100-day Lancozs bandpass filter to daily rainfall anomalies. The MISO index is defined as the standardized filtered rainfall anomalies averaged over central India (15°N-25°N, 70°E-85°E). This selection covers the narrow-tilted belt extending from the northern BoB to the Western Ghats and eastern AS over which maximum intra-seasonal variability in precipitation lies. Active (cycles) are defined as days when the MISO index is greater (less) +1(-1). Hovmöller analysis of rainfall anomalies for most significant (coherent) northward propagating MISOs is also carried out during the active phase of monsoon. Coherent MISO events which propagate from the equator to 20°N and bear similar phase structures at a given latitude are determined following Jiang et al. (2004), Ajayamohan et al. (2008), and Sabeerali et al. (2014). The longitudinally (85°E-95°E) averaged filtered rainfall anomalies (colour shading) for the coherent MISOs over BoB during the active phase of the monsoon are plotted in Fig.1(a)-(c). In observation, positive anomalies start over the southern BoB at -20 days and propagate northward to +10 days. The subsequent break phase with negative rainfall anomalies starts at southern BoB around the 0th day and propagates northward to higher latitudes up to +20 day. During the active phase, stronger positive rainfall anomalies can be seen over 10°N-20°N latitude during -10 to +10 days. A similar active phase followed by a break phase in rainfall anomalies can be seen in CFSv2 CTL simulations. However, significant differences in terms of amplitude, organization, and propagation of anomalies can be noted in the model. The propagation of MISO anomalies is slower in the model CTL simulation. The CTL simulated rainfall anomalies during the active phase of the monsoon are weaker in magnitude, specifically at higher latitudes. Li et al. (2018) reported rapid growth of errors in model-simulated MISO anomalies beyond 12°N. The problems mentioned above, related to MISO amplitude and propagation, are due to the errors in air-sea coupling in models as suggested by earlier studies (Wang et al. 2009; Sharmila et al. 2013; Srivastava et al. 2017; Li et al. 2018). Li et al. (2018) have also analyzed CFSv2 forecasts and have found that the air-sea interactions are underrepresented over the Arabian Sea and BoB during intra-seasonal oscillations. The amplitude of MISO was underestimated due to too weak SST response to surface fluxes and convection response to SST. They have suggested the inclusion of ocean skin layer and better resolving diurnal cycle as the ways to improve the MISO characteristics in coupled models. Therefore, this section addresses the impact of including diurnal skin temperature parameterization (SEN run) on simulating MISO amplitude and propagation characteristics. With the diurnal cycle of SST, stronger active and subsequent break phases are seen in the SEN compared to the CTL run. The positive rainfall anomalies during the active phase are stronger in SEN run from the equator to northern latitudes. Hovmöller analysis of rainfall anomalies centred around the peak break phase (figure not shown) shows that rainfall anomalies during both the break phase and the following active phase are significantly stronger, and they propagate to higher latitudes in SEN run (20°N) compared to CTL run (16°N). Therefore, in SEN simulations, the active phase after the break phase bears a better resemblance with the observed ones. The underlying mechanism for this difference in meridional propagation characteristics in the presence/absence of the SST diurnal cycle is further discussed.
3.2. MISO Mechanism
As discussed earlier, among various mechanisms proposed for poleward propagation of MISOs, "vertical wind shear" and "moisture-convection feedback" mechanisms postulated by Jiang et al. (2004) are widely accepted. These mechanisms examine the meridional relationship of various atmospheric fields linked to northward propagating MISOs. Meridional asymmetry in the vertical structure of circulation and convective parameters around the convection center are the prominent features supporting these mechanisms. Therefore, the vertical profiles of vertical velocity, specific humidity, vorticity, and divergence are composed at different latitudes with respect to the maximum convection center and are shown in Fig. 2. The vertical profiles are obtained by averaging over 80°E-95°E longitudes over BoB. The meridional structure of vertical velocity shows that maximum vertical motion is located at the convection center and occurs in the middle troposphere (around ~500 hPa). A northward shift of vertical motion at a lower level can be seen in Fig. 2(a), resulting in tilting the maximum vertical velocity axis. The northward shift of the maximum vertical velocity axis is extended up to 6° north of the convection center. The ascending motion is associated with a low-level convergence and upper-level divergence, as shown in Fig. 2(d). The maximum upper-level divergence is collocated with the convection center, whereas the maximum low-level convergence leads the convection center by a few degrees. In the specific humidity profile (Fig 2. g), the maxima lie around 700 hPa in the reanalysis. A poleward shift similar to vertical velocity is seen in the axis of maximum specific humidity. The specific humidity profile tilts at lower levels up to 2° north of the convection center. The vorticity field shows a clear meridional asymmetric structure around the convention center. An equivalent barotropic positive vorticity is located north of the convection center, whereas similar equivalent barotropic negative vorticity is located south of the convection center. The positive barotropic vorticity is located 2° north of the convection center. A similar northward shift is also seen in the vertical profile of geopotential height (Supplementary 1). The meridional structure of the vertical profile of Moist static energy (MSE) resembles that of specific humidity with maxima located around 5° north of the convection center and tilting of maximum vertical MSE axis in the lower atmosphere (Supplementary 1). These observed features are similar to that of reported earlier studies with insignificant differences due to the different study periods and reanalysis dataset considered in this study. Based on these features, Jiang et al. (2004) proposed that during the active phase of MISO, a baroclinic divergent motion (i.e., upper-level divergence and lower-level convergence) with maximum vertical motion in the middle troposphere appears because of the convective heating in the middle troposphere. The interaction between this baroclinic divergence and a strong easterly shear in the monsoon regions results in a positive (negative) barotropic vorticity north (south) of the convection center. The positive barotropic vorticity further develops a free-atmosphere divergence north of the convection center. As a result, boundary layer convergence increases north of the convection center (due to Ekman pumping). The low-level moisture convergence shifts the center of convective heating to the north of the previous convection center. Therefore, dynamical features essential for coherent northward propagation of MISO can be summarised as (a) Meridional asymmetry in vertical profiles of vertical velocity, divergence, vorticity, specific humidity, and geopotential height. (b) northward shift of the axis of maximum at a lower level in various parameters such as vertical velocity, vorticity, specific humidity, geopotential height, and moist static energy (MSE; Supplementary-1).
It was discussed earlier that the phase and amplitude of MISOs are better simulated in the presence of the diurnal cycle of the sea surface. Therefore, we further analyze whether the dynamical features necessary for MISO propagation are improved in the presence of diurnal SST. In Fig. 2, the middle panel shows the vertical structure of various parameters around the convection center. The meridional asymmetry and northward shift in these parameters showing boundary layer convergence leading to the convection center are reasonably well simulated by CFSv2 (CTL) simulations. However, a few limitations compared to observation can be noted, such as the axis of maximum vertical velocity, specific humidity, and moist static energy do not show northward tilt at lower levels as observed in reanalysis. Also, the extent of the northward shift of ascending motion and boundary layer convergence is smaller in the CTL simulation than in the reanalysis. From SEN run with the diurnal cycle over oceans, the tilt in maximum ascending motion at the lower level is seen and is better simulated as it shifts around 6° (~2° more than the CTL run) north of the convection center. The divergence plot also shows the intensification of lower-level convergence and upper-level divergence in the SEN run as compared to the CTL run. A clear northward shift of maximum lower-level convergence can also be seen in the SEN run (1.5°), unlike that of the CTL run (0.5°). The north-south extension of moisture availability with a farther northward shift of maximum specific humidity in the SEN run is similar to reanalysis, which was a major limitation in CTL simulations. The axial tilt in specific humidity is also better represented in SEN. Therefore, the vertical profiles of specific humidity and divergence in CTL and SEN run indicate a stronger anomalous moisture convergence when the diurnal cycle of SST is implemented. Comparing the vertical profiles of vorticity shows that the positive barotropic vorticity is shifted north of the convection center in SEN run compared to the CTL run. Therefore, the presence of a diurnal cycle in SST helped towards a better simulation of dynamical features required for coherent poleward propagation of MISOs. The next section will discuss how both simulations compare the air-sea interaction processes during the MISO life cycle.
3.3 Air-Sea Interaction
The critical role of SST and air-sea interactive fluxes during the coupled evolution and northward propagation of monsoon intra-seasonal oscillations have been extensively studied by researchers in the past (Shinoda et al. 1998; Kemball-Cook and Wang 2001; Sengupta et al. 2001; Fu et al. 2003; Ajayamohan et al. 2008; Li et al. 2018). The studies mentioned above have shown the lead-lag relations between SST, surface net heat flux (Qnet), and convective anomalies during different phases of intra-seasonal oscillation over the Indian Ocean, BoB, and AS. To evaluate the role of the diurnal cycle of SST on the northward propagation of MISOs, further analysis of air-sea interaction characteristics is carried out. In Fig.1(a)-(c), the contours represent the filtered SST anomalies during the active spell over central India. Warmer (cooler) SST anomalies before (after) the active phase can be seen in observation and are in line with earlier studies (Fu et al. 2003; Li et al. 2018). At the intra-seasonal scale, Qnet drives the intra-seasonal SST changes during the coupled evolution and northward propagation of monsoon intra-seasonal oscillations (Shinoda et al. 1998; Sengupta al. 2001). During monsoon season, over the BoB, variability in latent heat flux and solar radiation dominates towards Qnet variability over all other heat fluxes. Fig.1 (d) shows the filtered Qnet anomalies as shading and filtered LHF anomalies as contours in reanalysis during the coherent propagation of MISO. The convention used for Qnet and LHF is Qnet is positive downward, and LHF is positive upward. Qnet anomalies are approximately out of phase with convection, where negative (positive) Qnet anomalies cooccur with positive (negative) precipitation anomalies. The net heat flux anomalies are also in quadrature with SST anomalies with positive Qnet leading warmer SST anomalies. The latent heat flux varies out of phase with Qnet, and negative LHF anomalies are seen before the active spell resulting in warmer SST anomalies. Therefore, during the break spell, Qnet increases due to the combined effect of reduced LHF (due to weaker winds) and increased solar radiation. The enhanced heat in the ocean causes the sea surface to warm. Although these warmer SSTs can be a response to the break phase due to clear sky conditions, they can help initiate and propagate active spell (Sengupta et al. 2001; Ajayamohan et al. 2008) by destabilizing the lower atmosphere (Lindzen and Nigam 1987; Roxy and Tanimoto 2007). Fig.1 (g) shows the convergence terms of column integrated moist (colour shading) and MSE (contour) budget equation. The figures show enhanced (positive anomalies) moisture convergence posterior to the warm SST anomalies and during active spells. On the other hand, the recharge of moist static energy through MSE convergence during the preceding break and discharge of moist static energy through MSE divergence can also be noted. Therefore, during the monsoon break phase, MSE builds up due to enhanced Qnet and warming, causing increased boundary layer convergence.
Comparing model simulations (Fig.1) against the observation/reanalysis indicates that the model's lead-lag relation between ocean, atmosphere and air-sea interaction parameters are satisfactorily well represented. But significant differences in the magnitude organization of anomalies can be noted between the two model simulations. The warmer SST anomalies before a stronger active phase are seen (Fig.1 b-c) in the SEN run (~0.3°C) compared to the CTL run (~0.25°C). Also, SST anomalies are cooler in SEN run than CTL run posterior to the active phase. The reason for warmer SSTs before the active spell in SEN run is due to the better representation of rectification of intra-seasonal SSTs (discussed in the following sections) by diurnal warming during the break phase of the monsoon. Rectification is the process of enhancement of intra-seasonal SST variability by diurnal warming and is reported in observational (Mujumdar et al. 2011; Yan et al. 2021) as well as modelling studies (Shinoda 2005; Bernie et al. 2007; Guemas et al. 2011). During the suppressed convection, the surface winds are weak, along with higher solar radiation due to less cloud cover. In these conditions, the weak shear-driven mixing is stabilized by enhanced buoyancy due to the absorption of solar radiation. As a result, the shallow mixed layer rapidly warms up with net heat gain. Therefore, during the suppressed phase, the amplitude of diurnal warming is significantly higher. The enhanced (reduced) diurnal warming during suppressed (active) phase can increase (decrease) the daily mean SST, and therefore it can enhance the magnitude of intra-seasonal SST variability. Hence, with the implementation of diurnal skin temperature parameterization, the intra-seasonal SST variability in SEN run gets amplified compared to the CTL run, which does not have diurnal warm-layer-cool-skin temperature parameterization. The underlying mechanism of warmer SSTs in the presence of diurnal skin temperature schemes is reflected in intra-seasonal anomalies of MLD (figure not shown), Qnet (Fig.1 e-f), LHF (Fig.1 e-f) intra-as well. The warmer SST anomalies during the break spell in the SEN run are associated with reduced LHF, enhanced Qnet, and shallower MLD anomalies compared to the CTL run. During the active phase, the associated convective downdrafts in the SEN run can cause a drier boundary layer and cooler surface air (Chen and Houze 1997). Hence, it increases the air-sea temperature and humidity difference, enhancing air-sea interactive fluxes. The stronger winds during a convective period can enhance air-sea flux anomalies. As discussed earlier, the surface heat fluxes and SSTs can modulate the boundary layer convergence, atmospheric stability, and atmospheric energy budgets; a similar impact is evident from Fig. (h)-(i) where convergence terms of moisture (shading) and MSE (contours) energy budgets are plotted as Hovmöller diagrams for CTL and SEN simulations respectively. Enhanced moisture and MSE convergence anomalies throughout northward propagation of MISOs in the SEN run are observed compared to the CTL run. These observations are consistent with the rectification of SSTs in SEN run by by diurnal warming, which plays an important role during the life cycle of MISO by modulation of air-sea fluxes, boundary layer convergence, energetics, and convection.
3.4. Rectification
The previous section highlighted the importance of intra-seasonal SST anomalies on the northward propagation of intra-seasonal anomalies. Based on these discussions, the question arises of why the intra-seasonal SST variability is amplified in SEN run with the implementation of the diurnal cycle of the sea surface. Therefore, the present section addresses why and how the diurnal cycle is expected to impact the intra-seasonal SST variability and related surface and atmospheric processes. Earlier studies, (e.g. Kawai and Wada 2007; Brunke et al. 2008; Pradhan et al. 2022) have shown how the parameterization of the diurnal cycle of SST and air-sea interactive fluxes can improve the diurnal variability of ocean-atmosphere parameters, as well as seasonal and interannual variability in coupled model simulations. The scale interaction between SST at diurnal and longer time scales can be quantified in terms of the persistence of diurnal warming, and is evaluated by computing decorrelation time. The decorrelation time is defined (Guemas et al. 2011) as the time (in days) for which the lagged correlation between diurnal warming (DW) and SST remains significant at a critical level (95%) of significance. Therefore, persistence values indicate to what temporal extent diurnal warming can interact with slower scales. Fig. 3 presents the persistence values over the Indian and Pacific Oceans where Indo-Pacific tropical moored buoys are located. In the tropical Indo-Pacific basin, the observed persistence is mostly greater than 15 days and ranges up to 60 days at a few locations. Both the model simulations could reproduce the persistence values greater than 15 days in most of the Indo-Pacific tropical Ocean. Therefore, diurnal warming in observation and model simulations can impact the intra-seasonal and seasonal SST variabilities. However, some differences between observation and model-simulated persistence patterns can be noticed. For example, observed persistence is higher over the central Pacific Ocean and western Pacific warm pool region than the eastern Pacific Ocean. In CTL simulation, the persistence is higher over the central and eastern Pacific oceans. Therefore, the persistence values are underestimated over the central and western Pacific region and overestimated near the eastern Pacific Ocean. The persistence in SEN run is significantly better than CTL run as it is closer to observation in the western Pacific warm pool region and over the eastern and central Pacific oceans. On the other hand, over the Indian Ocean, both CTL and SEN run agree reasonably well with observations. Since, for most of the regions considered in this study, the diurnal warming persists more than 15 days and can impact the intra-seasonal SST variability, therefore further analysis is carried out to quantify the amplitude contribution of diurnal warming to intra-seasonal SST.
The rectification mechanism through which diurnal SSTs can amplify/subdue the intra-seasonal amplitude of SST has been proposed and discussed in various observational and modelling studies (Shinoda and Hendon 1998; Bernie et al. 2005; Mujumdar et al. 2011; Yan et al. 2021). In this study, the amplitude of rectification by diurnal cycle is computed as
ISVwithout is calculated as the standard deviation of time series of the night time minimum temperature (otherwise know as foundation SST) which is assumed to be independent of diurnal cycle, whereas ISVwith is calculated as the standard deviation of hourly and 3-hourly SST dataset in observation and model respectively. Therefore, ISVwith and ISVwithout are the intraseasonal standard deviations of SST with and without diurnal cycle, respectively. The numerator of Equation-1 is equivalent to intraseasonal standard deviation of diurnal SST and the ratio describes the contribution (in percentage) of diurnal SST to the intraseasonal variability of total SST. The observed and model-simulated amplitude of rectification is shown in Fig 4 at various buoy locations. The observed contribution is found to be positive over the western tropical Pacific Ocean and Indian Ocean and negative over the equatorial eastern Pacific Ocean. These findings agree with the previous study of Yan et al. (2021), with a minor difference in magnitude because of the difference in the analysis period. In the present study, only buoys having continuous high-frequency (hourly) data for at least five years are considered, while Yan et al. (2021) have not considered such criteria. The diurnal SST tends to enhance intra-seasonal SST variability over Indo-Pacific warm pool region, whereas it weakens the intra-seasonal variability over the eastern equatorial Pacific Ocean. Such asymmetric association of diurnal and intra-seasonal SST is due to differential air-sea interactions at the eastern and western Pacific Oceans, as suggested by Yan et al. (2021). Over the western equatorial Pacific, ocean is highly governed by atmospheric processes, whereas over the eastern equatorial Pacific, the atmospheric processes are governed by oceanic processes. In the eastern equatorial Pacific region, the warmer (cooler) SSTs are favorable for enhanced (reduced) convection with stronger (weaker) winds which reduces (enhances) the amplitude of diurnal SST. Therefore, intraseasonal SST and diurnal SST are in opposite phase with each other over the equatorial cold tongue region. On the other hand, over the western equatorial Pacific region, due to enhanced (reduced) convection with stronger (weaker) winds both SST and diurnal SST are reduced (enhanced). Therefore, intraseasonal SST and diurnal SST are in same phase with each other over the western Pacific warm pool region. The comparison of model simulations against the observation indicates that throughout the Indo-Pacific basin, the rectification is weaker, i.e., underestimated in the CTL run. In contrast, the same is improved and closer to observation in the SEN run. The observed amplitude of rectification over the tropical western Pacific region is 8-10%, whereas the same in the CTL run is 2-3%. But in the SEN run, the amplitude of rectification is significantly enhanced and ranges between 3-10%. Also, the CTL simulation shows a weakening of intraseasonal SST variability due to diurnal SST at various locations (between 5°S-0°N and 150°E-170°E) over the western Pacific Ocean which is not realistic. At these locations, CTL run produces negative rectification whereas SEN run produces positive rectification similar to observation. Therefore, the SEN simulation is improved and realistic with the revised flux and skin temperature scheme. Over the northern Indian Ocean also, the amplitude of rectification is enhanced in SEN run compared to the CTL run and is closer to the observed amplitude. Therefore, the more accurate persistence and amplitude of SST rectification seen in the presence of diurnal skin temperature parameterization can eventually lead to a better representation of air-sea interaction and convection during different phases of MISO. The diurnal warm layers over the BoB are strong (Mujumdar et al., 2011) and to study them high frequency observations of ocean state are needed. But continuous high frequency observation through buoy network in Indian ocean is very poor. Hence, a complete picture of rectification throughout the Indian Ocean could not be not be represented in this study.
3.5. Diurnal Sea Surface Warming and its relation to the atmosphere
Bellenger et al. (2010) used 30 days of in situ observations and showed the possible association of diurnal sea surface warming with atmospheric boundary layer and convective processes. Most of their discussion is confined to addressing the diurnal behaviour of convective features in the presence/absence of diurnal warm layers. However, their results (specifically Fig 3 of their study) also showed that subdued convective processes and calm wind conditions accompany diurnal warming events. Strong diurnal warming events are found to be associated with reduced daily mean latent/sensible heat, reduced horizontal wind, reduced downdraft, shallow atmospheric mixed layer, and reduced precipitation. In the current section, analysis is carried out to validate these inferences and to see how these associations are simulated without and with diurnal skin temperature parameterization. Composite analysis of atmospheric fields is carried out by defining strong diurnal warming (SDW) and weak diurnal warming (WDW) events. SDW(WDW) events are determined as the days when the diurnal range of SST (dSST) is greater (less) than 1(-1) standard deviation from its seasonal mean. Fig. 5 shows the composite horizontal wind speed at 10m during SDW and WDW events. From observation, it is evident that during SDW events, the horizontal winds are calmer over the Indo-Pacific Ocean than during WDW events. However, stronger winds along the Somalia jet region region can be seen during strong warming events compared to other regions. On the other hand, relatively weaker winds are seen over the equatorial Indo-Pacific regions compared to other regions during weak warming days. Comparing model simulations against the observation indicates that CTL simulation produces stronger winds over off-equatorial regions during strong warming days compared to observations. On the other hand, the SEN run with diurnal SST parameterization reproduces the wind conditions over the Indo-Pacific basin realistically closer to observation. During WDW events, the model simulations agree with observation except for the underestimation of wind speed over the north-Pacific Ocean in CTL simulations. Similarly, a composite of surface latent heat flux during SDW and WDW days for observation and simulations is plotted in Fig. 7. Observation shows the magnitude of latent heat flux is lower during SWD days than DWD days. This agrees with Bellenger et al. (2010), who have shown reduced daily mean latent heat during strong diurnal warming days. The higher daily mean latent heat flux during WDW days is well reproduced by both the model simulations with overestimation in magnitude in both CTL and SEN. However, during SDW days, the CTL simulations significantly overestimate the latent heat flux compared to observation and SEN simulations. In the CTL run, no clear difference in latent heat fluxes is noticed between SDW and WDW days. The overestimation of latent heat flux during WDW events can also be linked to the unrealistic higher wind speeds simulated by CTL simulations, as discussed in Fig. 5. However, due to the presence of diurnal SST parameterization along with COARE 3.0 flux scheme, the latent heat flux simulation is significantly better in SEN run compared to CTL run specifically during WDW days. Further analysis is carried out to see the impact of diurnal warming on convective processes. The composite of daily mean precipitation is plotted in Fig. 6 during SDW and WDW days for observation and model simulations. Reduced rainfall during SDW events and enhanced rainfall over the tropical Indian Ocean and western and eastern Pacific Ocean during WDW events can be seen from observed rainfall composites. As suggested by Fairall et al. 1996 (and references therein), diurnal warming is stronger during clear skies and calm wind conditions. In the CTL run, the simulated rainfall over the tropical eastern Pacific and western Pacific warm pool region during SDW days is of higher magnitude and unrealistic. On the other hand, SEN run realistically produced reduced convection over the Indo-Pacific Ocean. The simulated rainfall patterns during WDW events are similar in CTL, and SEN runs with minor underestimation of rainfall magnitude in CTL run over the equatorial Indo-Pacific Ocean.
Chen and Houze (1997) suggested that convective downdrafts can cause a drier boundary layer and cooler surface air. Hence, it increases the air-sea temperature and humidity difference, enhancing air-sea interactive fluxes. The gusty winds during a convective period can also enhance the air-sea fluxes. These convective features are associated with a reduction in daytime warming in SST. The observed winds, precipitation, and latent heat flux, shown in Fig. 5-7, indicated similar inferences where stronger winds, enhanced precipitation, and enhanced latent heat fluxes are found during weak diurnal warming days. Also, the comparison of model simulations confirms that diurnal skin temperature parameterization is important to simulate a realistic association between the diurnal variability of the sea surface and the atmospheric and air-sea interface.