Impact of a Mixed Ocean Layer and the Diurnal Cycle on Convective Aggregation

Abstract We investigate how ocean feedbacks and the diurnal cycle impact convective aggregation using a slab ocean coupled to a cloud resolving model. With a 20 m mixed layer ocean, aggregation occurs after 25 days. Thinner ocean layers slow the onset of clustering, with a 1 m ocean layer needing around 43 days. The delay is due to anomalous solar radiation in clear sky regions, causing a relative surface warming balanced by a matching cooling in cloudy areas. The resulting gradient in surface heat fluxes opposes low level convergence into convecting regions. On aggregation, the convective regions are surrounded by moist, clear sky regions with the hottest SSTs, toward which convection migrates, while a cold SST patch forms under dry suppressed regions due to enhanced latent heat fluxes and longwave radiation. The next experiment allows a diurnal cycle of 2.5°C in the domain mean SST. This causes convective rainfall to shift from a weak morning maximum to a sharper evening peak, reminiscent of undisturbed tropical observations. However, convection reverts to a weak early morning maximum once aggregation starts due to spatially heterogeneous radiative forcing. This implies thin mixed ocean layers are a necessary but non‐sufficient condition for an afternoon maximum of convection; limited spatial water vapor variability is also necessary. The imposition of the mean diurnal cycle has no statistically significant impact on the mean timing of clustering onset.


Introduction
This file contains a text overview of the experimental set up and parameterization choices, a summary figure for the performance of the neural network flux proxy model, and a figure illustrating how the adaptive Q-flux boundary condition allows a full diurnal cycle to be represented while removing any mean drift. Additional figures provide more supplementary information on the diurnal cycle and long-term evolution of the spatial mean and variance of the SST and well as the long term evolution of its variance. Figure S1. Offline integration of a toy slab ocean model with a mixing layer depth h=1 meter, and the seawater heat capacity of c pl =3850 J kg −1 K −1 and density ρ l =1020 kg m −3 . Three comparison methods are shown to control the SST, to illustrate how the new June 22, 2021, 6:48pm X -2 : adaptive SST control mechanism permits a full diurnal cycle while avoiding SST drift from the desired boundary condition, set to SST b = 28 o C as in the CRM simulations conducted in this paper. In panel a, an artificial surface net energy flux is constructed according to F = Acos((2t + 1)π) + I, where A is the flux amplitude set to 300 W m −2 here, t is the time in days and I is the flux imbalance, which is set to an illustrative value of 120 W m −2 , marked by the dashed line. In panel b, three simulations of the SST are made, all using a relaxation timescale τ of 24 hours to allow a diurnal cycle. SST -relax shows the resulting SST using a classic Newtonian relaxation where dSST /dt = (SST t − SST )/τ , and SST t is simply set to the target boundary temperature of SST b . In this case, the SST follows a diurnal cycle, but the SST drifts by τ I C pl ρ l h , more than 2K. In SST -offset, a modified value SST t = SST b − τĨ C pl ρ l h is used, using an (incorrect) estimate of the imbalancẽ I, which we set to 70 W m −2 for illustrative purposes. This reduces the drift but does not eliminate it due to the error inĨ (note that I would be constantly evolving with the model mean state). In SST -adaptive, a second prognostic equation is introduced dSST t /dt = (SST b − SST )/τ adj (see paper for more details), with SST the running mean of SST calculated using Welford's algorithm with a window of one day and τ adj =2 days.
Here the SST t , shown by the red line, undergoes a slightly under-damped second order response and brings the SST to equilibrium by day 10 with an error<0.01 K in the mean temperature with respect to SST b shown with the dashed line. Panel (c) is a repeat of panel (b) but with τ =12 hours, as used in this paper. This has the advantage of resulting in a faster adjustment to equilibrium and smaller drift in the first 3 days, but at the cost of a small damping of the diurnal cycle amplitude by about 4%.
June 22, 2021, 6:48pm   Red contours indicate rain rates of 10 and 25 mm day −1 . Note that instantaneous fields are sampled 4 times a day.
June 22, 2021, 6:48pm X -4 : Figure S5. Timeseries of the spatial standard deviation of the SST for member 3 and 4 of the (a) MLD-CONST, (b) MLD1-DIURN simulations and (c) the mean of the two ensemble members for each experiment. In the pre-onset, the MLD1-DIURN has a reduced diurnal cycle due to the fact that the convection occurs predominately during the afternoon, thus greater anvil shielding reduces the spatial heterogeneity of the SW surface flux relative to MLD-CONST, where convection occurs around the clock with a weaker nocturnal diurnal maximum. Only two members are shown to illustrate the cancellation of the diurnal cycle of variance that occurs during the clustering onset when the mean of the two is calculated (deep blue lines), which is due to the cycle reversing. In the pre-onset, solar heating causes the surface to be warmest in cloud free areas, leading to a variance maximum during the day. After clustering onset, the SST cools substantially under the dry patch and in this phase the day time heating offsets this and leads to a variance minimum during the day. The graph also reveals interesting long term oscillations in the SST variance and a reduction in the diurnal cycle. Text S1: Experimental set up Regarding the experiment set up, the domain size is 512 by 512 km, similar to Bretherton, Blossey, and Khairoutdinov (2005) with periodic lateral boundary conditions. (2012) found self-aggregation required domain sizes larger than 200 km although Tompkins and Craig (1998)  ration. Wing and Cronin (2016) introduced a theory for the spacing between convective clustered in organized states based on the boundary layer recovery that would suggest a single convective cluster is expected if convection organizes in a domain of this size. All model simulations use a 2 km horizontal spacing (as used by Tompkins & Craig, 1998;Bretherton et al., 2005;Muller & Held, 2012) and no convective parameterization scheme is used. A stretched vertical grid divides the atmosphere up into 62 layers. Domain-mean horizontal winds are constrained to be close to zero using a horizontally-homogeneous Newtonian relaxation term. This prevents the development of wind-shear during the simulation, as observed in previous simulations (Held et al., 1993;Tompkins & Craig, 1998;Tompkins, 2000), but does not impact the nature of convection or sub-domain circulations.

Muller and Held
In order to initiate convection in these simulations, a random perturbation is applied to the potential temperature field with amplitude of 0.1 K in the lowest level and linearly decreasing to 0.02 K in the fifth level.
Concerning the physical parameterizations used, the 5 th order advection scheme is employed for both momentum and scalar horizontal fields (Skamarock et al., 2008) and the microphysics is parameterized using the Purdue Lin scheme that includes six classes of hydrometers (water vapor, cloud water, rain, cloud ice, snow and graupel) (Lin et al., 1983).  (2017) that showed a strong propensity to undergo clustering.
X -8 : Figure S1. Offline integration of a toy slab ocean model with a mixing layer depth h=1 meter, and the seawater heat capacity of c pl =3850 J kg −1 K −1 and density ρ l =1020 kg m −3 .
Three comparison methods are shown to control the SST, to illustrate how the new adaptive SST control mechanism permits a full diurnal cycle while avoiding SST drift from the desired boundary condition, set to SST b = 28 o C as in the CRM simulations conducted in this paper. In panel a, an artificial surface net energy flux is constructed according to F = Acos((2t + 1)π) + I, where A is the flux amplitude set to 300 W m −2 here, t is the time in days and I is the flux imbalance, which is set to an illustrative value of 120 W m −2 , marked by the dashed line. In panel b, three simulations of the SST are made, all using a relaxation timescale τ of 24 hours to allow a diurnal cycle. SST -relax shows the resulting SST using a classic Newtonian relaxation where dSST /dt = (SST t − SST )/τ , and SST t is simply set to the target boundary temperature of SST b . In this case, the SST follows a diurnal cycle, but the SST drifts by τ I C pl ρ l h , more than 2K. In SST -offset, a modified value SST t = SST b − τĨ C pl ρ l h is used, using an (incorrect) estimate of the imbalanceĨ, which we set to 70 W m −2 for illustrative purposes. This reduces the drift but does not eliminate it due to the error inĨ (note that I would be constantly evolving with the model mean state). In SST -adaptive, a second prognostic equation is introduced dSST t /dt = (SST b − SST )/τ adj (see paper for more details), with SST the running mean of SST calculated using Welford's algorithm with a window of one day and τ adj =2 days. Here the SST t , shown by the red line, undergoes a slightly under-damped second order response and brings the SST to equilibrium by day 10 with an error<0.01 K in the mean temperature with respect to   where convection occurs around the clock with a weaker nocturnal diurnal maximum. Only two members are shown to illustrate the cancellation of the diurnal cycle of variance that occurs during the clustering onset when the mean of the two is calculated (deep blue lines), which is due to the cycle reversing. In the pre-onset, solar heating causes the surface to be warmest in cloud free areas, leading to a variance maximum during the day. After clustering onset, the SST cools substantially under the dry patch and in this phase the day time heating offsets this and leads to a variance minimum during the day. The graph also reveals interesting long term oscillations in the SST variance and a reduction in the diurnal cycle.