Diurnal Ocean Surface Warming Drives Convective Turbulence and Clouds in the Atmosphere

Sunlight warms sea surface temperature (SST) under calm winds, increasing atmospheric surface buoyancy flux, turbulence, and mixed layer (ML) depth in the afternoon. The diurnal range of SST exceeded 1°C for 24% of days in the central tropical Indian Ocean during the Dynamics of the Madden Julian Oscillation experiment in October‐December 2011. Doppler lidar shows enhancement of the strength and height of convective turbulence in the atmospheric ML over warm SST in the afternoon. The turbulent kinetic energy (TKE) dissipation rate of the marine atmospheric ML scales with surface buoyancy flux like previous measurements of convective MLs. The time of enhanced ML TKE dissipation rate is out of phase with the buoyancy flux generated by nocturnal net radiative cooling of the atmosphere. Diurnal atmospheric convective turbulence over the ocean mixes moisture from the ocean to the lifting condensation level and forms afternoon clouds.

moisture to the free troposphere when clouds were suppressed (LeMone & Pennell 1976). Cloud resolving models show an afternoon increase in shallow convective clouds over the warm SST anomalies (Ruppert & Johnson 2016).
Here we document the diurnal response of turbulence that connects dSST to convective clouds. Turbulence over marine convective atmospheric mixed layers (MLs) has been observed previously by aircraft (Fairall et al., 1980;Frisch & Ochs 1975;Lenschow 1970). Ship-based remote sensing allows us to profile the turbulence throughout the diurnal cycle. Intensification and deepening of the turbulent atmospheric ML were observed by Doppler lidar over dSST anomalies in the central Indian Ocean in late 2011 during the Dynamics of the Madden Julian Oscillation (DYNAMO) experiment (Section 2). The ML turbulence is shown to scale with the buoyancy flux like previously observed convective MLs, including diurnal mixing over land (Section 3). Section 4 shows the connection of the turbulent ML to the clouds and summarizes its effect on atmospheric moist convective clouds over the ocean.

The Diurnal Warm Layer of SST in the Indian Ocean
The DYNAMO experiment in November-December 2011 sampled two suppressed and active phases of precipitating convective clouds related intraseasonal atmospheric variability (Madden & Julian 1971). DYNA-MO days frequently had strong dSST. Median dSST was 0.58°C. The dSST was greater than 1°C for 19 (24%) of the 77 days, and greater than 1.5°C for seven of the days. Maximum dSST was 2.8°C. Diurnal warm layers did not form during two convective westerly wind bursts in late November (Figure 1b; Moum et al., 2014), but they formed on the days before, between, and after the wind bursts. The vertical structure of ocean DWLs was observed in DYNAMO from a ship (Hughes et al., 2020;Moulin et al., 2017), and by ocean gliders penetrating the surface (Matthews et al., 2014).
We focus on November 13-16, four consecutive days with dSST > 1.8°C (Figures 1b and 2b). These days were in the phase of suppressed intraseasonal precipitation (de Szoeke et al., 2015;Moum et al., 2014). At this time, weak winds reduced mechanical generation of turbulence in the atmosphere and the ocean and permitted stratification and warm SST anomalies to form in the ocean. SST warmed quickly during midday solar heating November 13-15 and cooled gradually at night (Figure 2d). On November 16, SST increased only modestly during mid-day and then quickly increased 2°C after 16 local time (LT). Quick cooling events related to 3-4.5 m s -1 gusts enhance the cooling during the afternoons of November 14 and 15.

Wind and Buoyancy Flux
Figures 1a and 1b shows the diurnal cycles of wind, solar radiation, ocean temperature at 0.1 and 5 m depth, and buoyancy flux for two month-long legs of the DYNAMO experiment (de Szoeke et al. 2015). Buoyancy flux at the surface depends on the temperature and water vapor flux, where T v is the virtual temperature T v =p/R d ρ=Tα, q is the specific humidity, β=R v /R d −1≈0.608, and H s , H l are the sensible and latent surface turbulent heat fluxes. Over the warm tropical Indian Ocean, the thermal expansion of air and the lower density water vapor both contribute comparably to the buoyancy flux. Temperature and water vapor flux are products of wind speed and the sea-air surface difference of temperature and humidity, respectively. Surface buoyancy flux B(0) observed in DYNAMO leg 3 (Nov 8-Dec 6, Figure 1b) Wind speed dominates daily to intraseasonal variability of the latent and sensible turbulent surface fluxes in DYNAMO (de Szoeke et al. 2015). Average buoyancy flux is weak (3 × 10 -4 m 2 s -3 ) for wind below 3 m s -1 (Figure 1b). Mean wind from 6 to 14 LT is less than 2.6 m s -1 on each of the 7 days with dSST > 1.5°C (Section 2a). The buoyancy flux is weaker on these days, yet the diurnal cycle of buoyancy flux is coherent, with maximum daylight buoyancy flux (6 × 10 -4 m 2 s -3 ) 2.7 times greater than the predawn (0-6 h local) mean buoyancy flux.
For November 13-17, the buoyancy flux is strongly correlated to the SST anomalies ( Figure 2b). The correlation coefficient R(SST, B) = 0.64 for Nov 13-17, and increases to R = 0.75 when computed for wind less than 3 m s -1 .

Turbulence Dissipation Rate Profiles
The diurnal enhancement of buoyancy flux generates turbulent convection in the subcloud boundary layer. The NOAA High-Resolution Doppler Lidar (C. J. Grund et al. 2001, Wulfmeyer & Janjić, ) measured the radial velocity of the air toward or away from the scanner. Vertical velocities in the subcloud boundary layer in DYNAMO were sampled by pointing vertically for 10 min every 20 min, alternated with constant elevation-angle azimuthal scans.
We estimate the turbulent kinetic energy (TKE) dissipation rate ϵ (Kolmogorov, 1941) in 10-min windows above 250 m (Figures 1c and 2c) from spectra of the inertial cascade of isotropic turbulence (Kaimal, 1973). Below 250 m, we estimate ϵ from transverse structure functions of the radial velocity from azimuthal scans ( Figure 2c; Frehlich et al., 2006). Further details of the observations, lidar scan strategy, and ϵ calculations are summarized in supplement S1. Examples of the horizontal velocity structures at night and in the afternoon are shown in supplement S2.
DE SZOEKE ET AL.
10.1029/2020GL091299 3 of 8 MLs with ϵ ≈ 10 -4 m 2 s -3 below a quiescent layer with much weaker turbulence ϵ < 10 -5 m 2 s -3 . We define the ML depth D as the lowest height at which ϵ is a factor of three smaller than the vertical mean ϵ below that height. ML depths were diagnosed for 2,008 profiles of ϵ in this manner (black dots Figure 2c). We define those MLs as convective that meet the threshold −D/L>100. One-third (658) of the MLs diagnosed in DYNAMO are convective according to this condition. The ratio −D/L is strongly dependent on the surface wind speed. Most of the convective MLs have surface wind speed less than 2 m s -1 . The ratio −D/L decreases approximately as wind speed U -3 in the shear-driven regime, and as U -2 in the convective regime (not shown), consistent with wind stress proportional to U 2 and buoyancy flux proportional to U (as in bulk aerodynamic models, e.g. Liu et al., 1979;Fairall et al., 1996).
The composite mean ϵ above the convective ML is 0.1B for our tropical marine atmosphere, larger than the previous studies (Figure 3). Moist convection driven by release of latent heat of condensation in clouds is responsible for intermittent turbulence above the ML. The distribution of ϵ is positively skewed (skewness of logϵ is 1-2), indicating infrequent strong events affect the mean. The median ϵ/B (0.05) agrees better with previous observations for 1.0 ≤ z/D' ≤ 1.4.

Discussion of the Mixed Layer TKE Dissipation Rate Profile
Our mean ϵ/B = 0.58 in the upper part of the convective ML is larger than ϵ/B = 0.4 predicted by the universal function for dissipation (observed for marine layers, e.g. by Lenschow et al., 1970). The median of our ϵ/B distribution is 0.4, suggesting that convective MLs matching the universal function are common within the turbulence measurements, but that ϵ is larger in the mean. In addition to the studies compared in Figure 3, convective cold air outbreaks over the Atlantic Ocean (Chou et al., 1986) and terrestrial convection (Luce et al., 2020, Figure 9) had ϵ ≈ 0.6B in the upper half of the ML.
There are several reasons the mean ϵ could be larger than the prediction for these convective MLs. Universal functions for ϵ (compiled by Kooijmans & Hartogensis 2016) are based on the convective parameter space 0<−z/L<5, but MLs in our study satisfy 40<−z/L. The universal functions apply to an entraining ML, in which ϵ equals the vertical mean buoyancy production 0.4B(0) of a linear profile B(z) = B(0)(1− 1.2z/D). Free entrainment with B(D) = 0 applies to the observed continuous transition to moist adiabatic stratification, in which case buoyancy production-dissipation balance gives ϵ/B = 0.5.
The universal function for ϵ assumes only surface shear and buoyancy flux produce TKE. Larger mean ϵ/B suggests episodic additional turbulence is generated aloft. Condensation in the intermittently cloudy moist adiabatic layer generates buoyancy flux. Cold evaporative downdrafts inject positive buoyancy flux and TKE into the ML, and cloud TKE can be transported into the ML. Figure 2c shows intermittent elevated layers of turbulence above D. Shear production linked to surface stress is negligible in the upper convective ML, yet

Connection of Diurnal Boundary Layer Convection to Clouds
The reconstructed convective ϵ is calculated by multiplying the normalized ϵ/B profile (Figure 3) by the time series of surface buoyancy flux B(0) for 2011 November 13-16 UTC (Figure 4a). The buoyancy flux, and hence the idealized convective ϵ in the ML, increases by a factor of 2.7 in the afternoon compared to at night.
Mixed layer depth is also deeper during the afternoon. Figure 4a shows D filtered thrice by a 180-min running mean. The afternoon maxima of D Nov 13-16 correspond to maxima in buoyancy flux ( Figure 4b) and convective ϵ (Figure 4a). When this deeper D reaches the LCL (also filtered, orange line Figure 4a), water vapor can condense and form a cloud at near the ML top (gray dots, Figure 4a; gray bars, Figure 4b, show cloud fraction below 1 km).
The ML depth falls below the LCL each evening after sunset. The LCL also lowers gradually at night due to lower temperature and higher relative humidity. The LCL reaches a minimum around dawn (about 0 UTC). The surface air dewpoint depression T−T d predicts LCL as z LCL = 40 m+(128 m/°C)(T−T d ).

Summary
Diurnal convective MLs over the ocean are like those over land but with weaker temperature and buoyancy flux anomalies. Weak wind simultaneously makes for weak shear and strong diurnal ocean surface temperature anomalies. The 4-day composite mean ϵ profile of diurnal convective MLs is 0.58 ± 0.02 times the surface buoyancy flux in the upper ML, scaling with surface buoyancy flux like previous observations of convective MLs in the atmosphere and oceans.
Diurnal convective turbulence generates clouds. ML depth is greatest during the afternoon when the SST is warmest and the mixed-layer ϵ is strongest. The ML depth reaches the lifting condensation level, where water vapor condenses and forms clouds. The measurements of the diurnal cycle of ϵ and D determine the turbulent fluxes into shallow clouds over the parts of the ocean experiencing weak wind, such as during phases of suppressed tropical convective precipitation.
DYNAMO had 24% of days with dSST > 1°C, more than most previous estimates. The fraction of days with dSST greater than 1°C varies widely among observational analyses. Higher-resolution satellite and in-situ measurements have higher dSST than reanalyzes (Bellenger & Duvel 2009;Clayson & Weitlich 2007). Extreme dSST from satellites exceeds 5°C (Clayson & Bogdanoff, 2013;Gentemann et al. 2003). Buoy observations from five tropical sites show dSST exceeds 1°C for 5% of days (Prytherch et al., 2013). This fraction of the oceans equatorward of 30° latitude would represent 2% of Earth's surface area.
DE SZOEKE ET AL.