Cloud-Radiation Interactions and Their Contributions to Convective Self-Aggregation 

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 km2 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:

\displaystyle \frac{1}{2}\frac{\partial\widehat{h'}_n^2}{\partial t} = \widehat{h'}_nLW'_n + \widehat{h'}_nSW'_n + \widehat{h'}_nSEF'_n - \widehat{h'}_n\nabla_h\cdot\widehat{\textbf{u}h_n}

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

We use the variance of \widehat{h}_n as our aggregation metric. Hovmöller plots of \widehat{h}_n are shown in Figure 1 for each of our SSTs. In these plots, \widehat{h}_n 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 \widehat{h}_n, and shows that the variance of non-normalised \widehat{h}_n is ~4 times greater for our 305 K simulations compared to our 295 K simulation. Figure 2b shows time series of the variance of \widehat{h}_n. 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 \widehat{h}_n variance around 10-4 or lower correspond to randomly scattered convection, whereas values greater that 10-3 are associated with strongly aggregated convection.

Figure 3: Maps of (a) cloud condensed water path, (b) vertically-integrated FMSE anomaly, (c) longwave heating anomaly, (d) shortwave heating anomaly. Snapshots at day 100 of the 300 K simulation.

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 \widehat{h}_n 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 \widehat{h'}_n, LW' and SW'. We can see SW' and \widehat{h'} are closely correlated since SW' 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. LW' 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 \widehat{h}_n 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 \widehat{h'}_n as a factor, which increases with aggregation by definition.

Figure 4: Terms in Equation 1 vs normalised FMSE variance for each SST

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 \widehat{h} variance. Therefore, shortwave heating contributes less to aggregation at higher SSTs because they contribute to a smaller fraction of \widehat{h} 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 \widehat{h'}_n 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 \widehat{h}_n variance between 3\times10^{-4} and 4\times10^{-4} and the Mature phase has \widehat{h} variance between 1.5\times10^{-3} and 2\times 10^{-3}. The contribution of longwave interactions with each cloud type to aggregation during these two phases is shown in Figure 5a, with their mean LW'\times\widehat{h'} covariance and fraction shown in Figures 5b & c.

Figure 5: Mean (a) contribution to the longwave term in Equation 1, (b) normalised longwave-FMSE covariance, (c) cloud fraction for the Growth phase (dots) and Mature phase (open circles). Data points for each category are in order of SST increasing to the right.

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 \widehat{h} environments. The clear regions are the most abundant category, have typically negative longwave heating anomalies and tend to occur in low \widehat{h} regions, so their LW'\times\widehat{h'} 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 LW'\times\widehat{h'} 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 LW'\times\widehat{h'} 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 Systems11(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 Sciences62(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 Climate31(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 Geophysics38(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 Letters42(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 Systems13, 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 Society142(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 Systems6(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 Systems12(9), e2020MS0021380. https://doi.org/10.1029/2020MS0021380 

The 2nd ICTP Summer School in Hierarchical Modelling of Climate Dynamics

Between the 1st and 12th July 2019, I attended the 2nd International Centre for Theoretical Physics (ICTP) Summer School in Hierarchical Modelling of Climate Dynamics at the ICTP guesthouse in Trieste, Italy. The focus of this summer school was on convective organisation and climate sensitivity, which is incredibly relevant to my PhD topic: Interactions between Radiation and Convective Organisation. So, I felt I had to attend this summer school (and not just because my lead supervisor, Chris Holloway, was one of the lead directors).

This was an international conference with staff and students coming together from all corners of the globe. In total there were 111 people attending the school, made up of 84 participants, 20 speakers and 7 directors. Without knowing anyone else going to this school (except my supervisor), I was initially a little apprehensive as I didn’t know what to expect but as soon as I met some of the other students I was put at ease. It was amazing to meet other people working on very similar projects to me, especially since my supervisor was the only other person I previously knew working on this convective organisation topic. So, it was great to not only make new friends but also meet potential future colleagues.

Group photo of all those involved in the summer school.

As expected, the schedule was pretty intense, with most days working from 9am until 6pm except for lunch and a couple of coffee breaks. The mornings consisted of a couple of lectures given by some of the leading experts in the field including Kerry Emanuel, Bjorn Stevens and Sandrine Bony, then in the afternoons we would do some group project work. In our groups of 4 or 5, we analysed some numerical model data, to study how convection organises within our model. I was surprised to find that our group tasks were very similar to what I’ve been doing for my first year, so I was a bit worried that we’d manage to do what I’ve been working on this past year within a couple of weeks! But actually, it ended up giving me almost too many new ideas for my own research! In the second week, each group then had to give a quick presentation on their work.

Talk by Kerry Emanuel about the consequences of climate change on our weather.

Each day, after the lectures and the group work, we were free to do what we wanted for the rest of the evening. With the venue being right on the coast, and with temperatures consistently between 26 – 32C in the day, it was perfect to relax by the sea or go for a swim. Or, if we were bored with the relentless supply of pasta in the canteen then we’d often go into town in search of pizza and of course gelato!

At the start of the second week, there was a poster session in which a lot of the participants brought posters to showcase their projects. This was the first time I’d presented my research at an event like this, so it was great to show what I’ve been working on in front of so many people. It was exciting to see so many people genuinely interested in my work and I got lots of useful feedback and ideas.

Presenting my work at the poster session.

So overall, this summer school far surpassed my expectations and I would strongly recommend attending a summer school if you get the chance. I learned so much through the lectures, the group work, through chatting to the professors and students and through presenting my work. I now have far too many ideas to explore with my research, probably more than I can realistically achieve! Perhaps the most valuable aspect of the school was being able to meet so many people working in this field. Since this topic is very niche, I have been very lucky to meet a very large proportion of the people working in the topic so I’m sure some of our paths will cross in the future and we will be able to collaborate on future projects.