*Kieran Pope – k.n.pope@pgr.reading.ac.uk*

Convective self-aggregation is the process by which initially randomly scattered convection becomes spontaneously clustered in space despite uniform initial conditions. This process was first identified in numerical models, however it is relevant to real world convection (Holloway et al., 2017). Tropical weather is dominated by convection, and the degree of convective aggregation has important consequences for weather and climate. A more organised regime is associated with reduced cloudiness, increased longwave emission to space (Bretherton et al., 2005), and a higher frequency of long-lasting extreme precipitation events (Bao and Sherwood, 2019).

Because of its relevance to weather and climate, self-aggregation has been the focus of many recent studies. However, there is still much debate as to the processes that cause aggregation. There is great variability in the rate and degree of aggregation between models, and there remains uncertainty as to how aggregation is affected by climate change (Wing et al., 2020). Previous studies have shown that feedbacks between convection and shortwave & longwave radiation are key drivers and maintainers of aggregation (e.g. Wing & Cronin 2016), and that interactive radiation in models is essential for aggregation to occur (Muller & Bony 2015).

This blog summarises results from the first paper from my PhD (Pope et al., 2021), where we develop and use a framework to analyse how radiative interactions with different cloud types contribute to aggregation. We analyse self-aggregation within a set of three idealised simulations of the UK Met Office Unified Model (UM). The simulations are configured in radiative-convective equilibrium over three fixed sea surface temperatures (SSTs) of 295, 300 and 305 K. They are convection permitting models that are 432 × 6048 km^{2} in size with a 3 km horizontal grid spacing. The simulations neglect the earth’s rotation, so they approximately represent convection over tropical oceans within a warming climate.

Our analysis framework is based on that used in Wing and Emanuel (2014) which uses the variance of vertically-integrated frozen moist static energy (FMSE) as a measure of aggregation. FMSE is a measure of the total energy an air parcel has if all the water (vapour and frozen) was converted to liquid, neglecting its velocity. Variations in vertically-integrated FMSE come from perturbations in temperature and humidity. As aggregation increases, moist regions get moister and dry regions get drier, so the variance of vertically-integrated FMSE increases.

The problem with using FMSE variance as an aggregation metric is that it is highly sensitive to SST. A warmer atmosphere can hold more water vapour via the Clausius-Clapeyron relationship. This means there is a greater difference in FMSE between the moist and dry regions for higher-SST simulations, so the variance of FMSE is typically much greater for higher SSTs. To account for this problem, we normalise FMSE between hypothetical upper and lower limits which are functions of SST. This gives a value of normalised FMSE between 0 and 1.

Wing and Emanuel (2014) derive a budget equation for the rate of change of FMSE variance which shows how different processes contribute to aggregation. By rederiving their equation for normalised FMSE , we get:

where is vertically-integrated FMSE, and are the net atmospheric column longwave and shortwave heating rates, is the surface enthalpy flux, made up of the surface latent and sensible heat fluxes, and is the horizontal divergence of the flux. Primes () indicate local anomalies from the instantaneous domain mean. The subscript () denotes a normalised variable which is the original variable divided by the difference between the hypothetical upper and lower limits of . The equation shows that the rate of change of variance (left hand side term) is driven by interactions between anomalies and anomalies in normalised net longwave heating, shortwave heating, surface fluxes and advection.

We use the variance of as our aggregation metric. Hovmöller plots of are shown in Figure 1 for each of our SSTs. In these plots, is averaged along the short axis of our domains. The plots show how initially randomly-distributed convection organises into bands which expand until the point where there are 4 to 5 quasi-stationary bands of moist convective regions separated by dry subsiding regions. This demonstrates that once our domains become fully-aggregated, the degree of aggregation appears similar. Figure 2a shows time series of each of the variance of , and shows that the variance of non-normalised is ~4 times greater for our 305 K simulations compared to our 295 K simulation. Figure 2b shows time series of the variance of . From this, we can see the convection aggregates faster as SST increases, yet the degree of aggregation remains similar via this metric once the convection is fully aggregated. Values of variance around 10^{-4} or lower correspond to randomly scattered convection, whereas values greater that 10^{-3} are associated with strongly aggregated convection.

To understand the processes contributing to aggregation, we have to look to Equation 1. We mainly focus on the two radiative terms on the right hand side. The terms show that regions in which the radiative anomalies and the anomalies have the same sign contribute to aggregation. We can start to get an intuitive understanding of this concept by looking at maps of these variables. Figure 3b-d show maps of , and . We can see and are closely correlated since is mainly determined by the shortwave absorption by water vapour. Clouds have little effect on the shortwave heating rates, with ~90% of the shortwave heating rate in cloudy regions being due to absorption by water vapour. is closely linked to cloud condensed water path (Figure 3a). This is because the majority of our clouds are high-topped clouds which, due to their cold cloud tops, are able to prevent longwave radiation escaping to space, so they are associated with positive longwave heating anomalies.

The sensitivity of the budget terms to both aggregation and SST can be seen in Figure 4. This figure is made by creating 50 bins of variance and then averaging the budget terms in space and time for each bin and for each SST. Where the terms are positive, they are helping to increase aggregation. Where they are negative, the terms are opposing aggregation. The terms tend to increase in magnitude since every term has as a factor, which increases with aggregation by definition.

In general, we find the longwave term is the dominant driver of aggregation, being insensitive to SST during the growth phase of aggregation. Once the aggregation is mature, the longwave term remains the dominant maintainer of aggregation, however its contribution to aggregation maintenance decreases with SST. The shortwave term is initially small at early times but becomes a key maintainer of aggregation within highly-aggregated environments. This is because humidity variations are initially small, so there is little variation in shortwave heating. Once the convection is aggregated, moist regions are very moist and dry regions are very dry, so there is a large difference in shortwave heating between moist and dry regions. The variations in shortwave heating remain very similar with SST, meaning shortwave heating anomalies contribute the same amount to non-normalised variance. Therefore, shortwave heating contributes less to aggregation at higher SSTs because they contribute to a smaller fraction of anomalies. The radiative terms are balanced by the surface flux term (negative because there is greater evaporation in dry regions) and the advection term (negative because circulations tend to smooth out gradients). The decrease in the magnitude of the radiative terms with SST is balanced by the surface flux and advection terms becoming more positive with SST.

To understand the behaviour of the longwave term, we define different cloud types based on the vertical profile of cloud, assigning one cloud type per grid box in a similar way to Hill et al. (2018). We define a lower and upper level pressure threshold, assigning cloud below the lower threshold to a “Low” category, cloud above the upper threshold to a “High” category, and cloud in between to a “Mid” category. If cloud occurs in more than one of these layers, then it is assigned to a combined category. In total, there are eight cloud types: Clear, Low, Mid, Mid & Low, High, High & Low, High & Mid, and Deep. We can then find each cloud type’s contribution to the longwave term by multiplying the cloud’s mean [Equation] covariance by its domain fraction.

To see how the cloud type contributions change with aggregation, we define a Growth phase and Mature phase of aggregation. The Growth phase has variance between and and the Mature phase has variance between and . The contribution of longwave interactions with each cloud type to aggregation during these two phases is shown in Figure 5a, with their mean covariance and fraction shown in Figures 5b & c.

We find that longwave interactions with high-topped clouds and clear regions drive aggregation during the Growth phase (Figure 5a). This is because high clouds are abundant, have positive longwave heating anomalies and occur in moist, high environments. The clear regions are the most abundant category, have typically negative longwave heating anomalies and tend to occur in low regions, so their covariance is positive. During the Growth phase, there is little SST sensitivity within each category. During the Mature phase, longwave interactions with high-topped cloud remain the main maintainer of aggregation however their contribution decreases with SST. This sensitivity is mainly because there is a greater decrease in high-topped cloud fraction with aggregation as SST increases. This also has consequences for the covariance of the clear regions. As high-topped cloud fraction reduces, the domain-mean longwave cooling increases. This makes the radiative cooling of the clear regions less anomalous, resulting in an increasingly negative covariance during the Mature phase as SST increases.

There is great variability in the degrees of aggregation within numerical models, which has important consequences for weather and climate modelling (Wing et al. 2020). With cloud-radiation interactions being crucial for aggregation, understanding how these interactions vary between models may help to explain the differences in aggregation. This study provides a framework by which a comparison of cloud-radiation interactions and their contributions to convective self-aggregation between models and SSTs can be achieved.

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REFERENCES

Bao, J., & Sherwood, S. C. (2019). The role of convective self-aggregation in extreme instantaneous versus daily precipitation. *Journal of Advances in Modeling Earth Systems*, **11**(1), 19– 33. https://doi.org/10.1029/2018MS001503

Bretherton, C. S., Blossey, P. N., & Khairoutdinov, M. (2005). An energy-balance analysis of deep convective self-aggregation above uniform SST. *Journal of the Atmospheric Sciences*, **62**(12), 4273– 4292. https://doi.org/10.1175/JAS3614.1

Hill, P. G., Allan, R. P., Chiu, J. C., Bodas-Salcedo, A., & Knippertz, P. (2018). Quantifying the contribution of different cloud types to the radiation budget in Southern West Africa. *Journal of Climate*, **31**(13), 5273– 5291. https://doi.org/10.1175/JCLI-D-17-0586.1

Holloway, C. E., Wing, A. A., Bony, S., Muller, C., Masunaga, H., L’Ecuyer, T. S., & Zuidema, P. (2017). Observing convective aggregation. *Surveys in Geophysics*, **38**(6), 1199– 1236. https://doi.org/10.1007/s10712-017-9419-1

Muller, C., & Bony, S. (2015). What favors convective aggregation and why? *Geophysical Research Letters*, **42**(13), 5626– 5634. https://doi.org/10.1002/2015GL064260

Pope, K. N., Holloway, C. E., Jones, T. R., & Stein, T. H. M. (2021). Cloud-radiation interactions and their contributions to convective self-aggregation. *Journal of Advances in Modeling Earth Systems*, **13**, e2021MS002535. https://doi.org/10.1029/2021MS002535

Wing, A. A., & Cronin, T. W. (2016). Self-aggregation of convection in long channel geometry. *Quarterly Journal of the Royal Meteorological Society*, **142**(694), 1– 15. https://doi.org/10.1002/qj.2628

Wing, A. A., & Emanuel, K. A. (2014). Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations. *Journal of Advances in Modeling Earth Systems*, **6**(1), 59– 74. https://doi.org/10.1002/2013MS000269

Wing, A. A., Stauffer, C. L., Becker, T., Reed, K. A., Ahn, M.-S., Arnold, N., & Silvers, L. (2020). Clouds and convective self-aggregation in a multi-model ensemble of radiative-convective equilibrium simulations. *Journal of Advances in Modeling Earth Systems*, **12**(9), e2020MS0021380. https://doi.org/10.1029/2020MS0021380