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

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.

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.

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.

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

Methane (CH4) is a potent greenhouse gas. Its ability to effectively alter fluxes of longwave (thermal-infrared) radiation emitted and absorbed by the Earth’s surface and atmosphere has been well studied. As a result, methane’s thermal-infrared impact on the climate system has been quantified in detail. According to the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5), methane has the second largest radiative forcing (0.48 W m-2) of the well-mixed greenhouse gases after carbon dioxide (CO2) (Myhre et al. 2013, See Figure 1).  This means that due to its change in atmospheric concentration since the pre-industrial era (from 1750 – 2011), methane has directly perturbed the tropopause net (incoming minus outgoing) stratospheric temperature-adjusted radiative flux by 0.48 W m-2, causing the climate system to warm.

However, an important effect is missing from the current IPCC AR5 estimate of methane’s climate impact – its absorption of solar radiation. In addition to longwave radiation, methane also alters fluxes of incoming solar shortwave radiation at wavelengths between 0.7 – 10 µm.

Until recently this shortwave effect had not been thoroughly quantified and as such was largely overlooked.  My PhD work focuses on quantifying methane’s shortwave effect in detail and aims to build upon the significant, initial findings of Etminan et al. (2016) and a more recent study by Collins et al. (2018).

Etminan et al. (2016) analysed methane’s absorption of solar near-infrared radiation (at wavelengths between 0.2 – 5 µm) and found that it exerted a direct instantaneous, positive forcing on the climate system, largely due to the absorption of upward scattered, reflected near-infrared radiation by clouds in the troposphere. Essentially, this processes results in photons taking multiple passes throughout the troposphere, which in turn results in increased absorption by CH4. Figure 2 shows the net (downwards minus upwards) spectral variation of this forcing at the tropopause under all-sky (i.e. cloudy) conditions. Here it is clear to see methane’s three key absorption bands across the near-infrared region at 1.7, 2.3 and 3.3 µm.

As Etminan et al. (2016) explain, following a perturbation in methane concentrations all of these bands decrease the downwards shortwave radiative flux at the tropopause, due to increased absorption in the stratosphere. However, the net sign of the forcing depends on whether this negative contribution compensates over increased absorption by these bands in the troposphere (which constitutes a positive forcing). As Figure 2 shows, whilst the 3.3 µm band has a strongly net negative forcing due to the absorption of downwelling solar radiation in the stratosphere, both the 1.7 µm and 2.3 µm bands have a net positive forcing due to increased CH4 absorption in an all-sky troposphere. When summed across the entire spectral range, the positive forcing at 1.7 µm and 2.3 µm dominates over the negative forcing at 3.3 µm – resulting in a net positive forcing. Etminan et al. (2016) also found that the nature of this positive forcing is partly explained by methane’s spectral overlap with water vapour (H2O). The 3.3 µm band overlaps with a region of relatively strong H2O absorption, which reduces its ability to absorb shortwave radiation in the troposphere, where high concentrations of H2O are present. However, both the 1.7 µm and 2.3 µm bands overlap much less with H2O, and so are able to absorb more shortwave radiation in the troposphere.

My work aims to address these uncertainties by investigating the impact of factors such as updates to the HITRAN spectroscopic database (which provides key spectroscopic parameters for climate models to simulate the transmission of radiation through the atmosphere), the inclusion of the solar mid-infrared (7.7 µm) band in calculations of the shortwave effect and potential sensitivities, such as the vertical representation of CH4 concentrations throughout the atmosphere and the specification of land surface albedo. My work also extends Etminan et al. (2016) by investigating the shortwave effect at a global spatial resolution, since a two-atmosphere approach (using tropical and extra-tropical profiles) was employed by the latter. To do this I use the model SOCRATES-RF (Checa-Garcia et al. 2018) which computes monthly-mean radiative forcings at a global 5° x 5° spatial resolution using a high resolution 260-band shortwave spectrum (from 0.2 – 10 µm) and a standard 9-band longwave spectrum.

Initial results calculated by SOCRATES-RF confirm that methane’s all-sky tropopause shortwave radiative forcing is positive and that the inclusion of shortwave bands serves to increase the stratospheric-temperature adjusted longwave radiative forcing. In total my calculations estimate that the shortwave effect increases methane’s total radiative forcing by 10%. Whilst this estimate is lower than the 15% proposed by Etminan et al. (2016) it’s important to point out that this SOCRATES-RF estimate is not a final figure and investigations into several key forcing sensitivities are currently underway. For example, methane’s shortwave forcing is highly sensitive to the vertical representation of concentrations throughout the atmosphere. Tests conducted using SOCRATES-RF reveal that when vertically-varying profiles of CH4 concentrations are perturbed, the shortwave forcing almost doubles in magnitude (from 0.014 W m-2 to 0.027 W m-2) when compared to the same calculation conducted using constant vertical profiles of CH4 concentrations. Since observational studies show that concentrations of methane decrease with height above the tropopause (e.g. Koo et al. 2017), the use of realistic vertically-varying profiles in forcing calculations are essential. Highly idealised vertically-varying CH4 profiles are currently employed in SOCRATES-RF, which vary with latitude but not with season. Therefore, the realism of this representation needs to be validated against observational datasets and possibly updated accordingly.

Another key sensitivity currently under investigation is the specification of land surface albedo – a potentially important factor controlling the amount of reflected shortwave radiation absorbed by methane. Since the radiative properties of surface features are highly wavelength-dependent, it is plausible that realistic, spectrally-varying land surface albedo values will be required to accurately simulate methane’s shortwave forcing. For example, vegetation and soils typically tend to reflect much more strongly in the near-infrared than in the visible region of the solar spectrum, whilst snow surfaces reflect much more strongly in the visible (see Roesch et al. 2002). Currently in SOCRATES-RF, globally-varying, spectrally-constant land-surface albedo values are used, derived from ERA-Interim reanalysis data.

Figure 3 compares the spatial distribution of methane’s annual-mean all-sky tropopause shortwave forcing as calculated by SOCRATES-RF and Collins et al. (2018). Both calculations exhibit the same regions of maxima across, for example, the Sahara, the Arabian Peninsula, and the Tibetan Plateau. However, it is interesting to note that the poleward amplification shown by SOCRATES-RF is not evident in Collins et al. (2018). The current leading hypothesis for this difference is the fact that the land surface albedo is specified differently in each calculation. Collins et al. (2018) employ spectrally-varying surface albedo values derived from satellite observations. These are arguably more realistic than the spectrally-constant values currently specified in SOCRATES-RF. The next step in my PhD is to further explore the interdependence between methane’s shortwave forcing and land-surface albedo, and to work towards implementing spectrally-varying albedo values into SOCRATES-RF calculations. Along with the ongoing investigation into the vertical representation of CH4 concentrations, I aim to finally deliver a more definitive estimate of methane’s shortwave effect.

References:

Checa-Garcia, R., Hegglin, M. I., Kinnison, D., Plummer, D. A., and Shine, K. P. 2018: Historical tropospheric and stratospheric ozone radiative forcing using the CMIP6 database. Geophys. Res. Lett., 45, 3264–3273, https://doi.org/10.1002/2017GL076770

Collins, W. D. et al, 2018: Large regional shortwave forcing by anthropogenic methane informed by Jovian observations, Sci. Adv. 4, https://doi.org/10.1126/sciadv.aas9593

Etminan, M., G. Myhre, E. Highwood, K. P. Shine. 2016: Radiative forcing of carbon dioxide, methane and nitrous oxide: a significant revision of methane radiative forcing, Geophys. Res. Lett., 43, https://doi.org/10.1002/2016/GL071930

IPCC, 2013: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 1535 pp

Myhre, G., et al. 2013: Anthropogenic and natural radiative forcing, in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T. F. Stocker et al., pp. 659–740, Cambridge Univ. Press, Cambridge, U. K., and New York.

Roesch, A., M. Wild, R. Pinker, and A. Ohmura, 2002: Comparison of spectral surface albedos and their impact on the general circulation model simulated surface climate, J. Geophys. Res., 107, 13-1 – 13-18, https://doi.org/10.1029/2001JD000809

## The Colour of Climate

Email: Jake.J.Gristey@noaa.gov

Gristey, J.J., J.C. Chiu, R.J. Gurney, K.P. Shine, S. Havemann, J. Thelen, and P.G. Hill, 2019: Shortwave Spectral Radiative Signatures and Their Physical Controls. J. Climate, 32, 4805–4828, https://doi.org/10.1175/JCLI-D-18-0815.1

Sunlight reaching the Earth is comprised of many different colours, or wavelengths. Some of these wavelengths cannot be detected by the human eye, such as the ultraviolet (UV) wavelengths which famously cause sunburn. Fortunately for us, the most intense sunlight is found at harmless visible wavelengths and reaches the surface with relative ease, allowing us to see during the daytime. Sometimes nature aligns to dramatically separate these wavelengths, producing beautiful optical phenomena such as rainbows. More often, however, the properties of the atmosphere and surface lead to intricate differences in the wavelengths of sunlight that get reflected back to space (Fig. 1).

Satellites have observed specific wavelengths of reflected sunlight to infer the properties and evolution of our climate system for decades. Satellites have also independently measured the total amount of reflected sunlight across all wavelengths to track energy flows into and out of the Earth system. It has been less common to make spectrally resolved measurements at many contiguous wavelengths throughout the solar spectrum. In theory, these measurements would simultaneously provide the total energy flow – by integrating over the wavelengths – and the “spectral signature” associated with all atmospheric and surface properties that determined this energy flow. Our recent study puts this theory to the test.

Almost 100,000 spectra of reflected sunlight were computed at the top-of-atmosphere under a diverse variety of conditions. Applying a clustering technique to the computed spectra (which identifies “clusters” in a dataset with similar characteristics) revealed distinct spectral signatures. When we examined the atmospheric and surface properties that were used to compute the spectra belonging to each spectral signature, a remarkable separation of physical properties was found (Fig. 2).

Surprisingly, the separation of physical properties by distinct spectral signatures, as shown in Fig. 2, was found to be robust up to the largest spatial scales tested of 240 km. This is similar to the footprint size of one of the only previous satellite instruments to measure contiguous spectrally resolved reflected sunlight, the SCIAMACHY**, providing an exciting opportunity to investigate spectral signature variability in real observations. We found that the frequency of spectral signatures in real SCIAMACHY observations followed the expected behaviour during the West African monsoon very closely (Fig. 3).

Overall, the separation of physical properties by distinct spectral signatures demonstrates great promise for monitoring evolution of the Earth system directly from spectral reflected sunlight in the future.

Funding acknowledgement: This work was supported by the Natural Environment Research Council (NERC) SCience of the Environment: Natural and Anthropogenic pRocesses, Impacts and Opportunities (SCENARIO) Doctoral Training Partnership (DTP), Grant NE/L002566/ 1, and from the European Union 7th Framework Programme under Grant Agreement 603502 [EU project Dynamics–Aerosol–Chemistry–Cloud Interactions in West Africa (DACCIWA)]

*Note several key simplifications in Fig. 1 for the purposes of visual effect: atmospheric properties are separated, but often occur simultaneously and throughout the atmosphere; the depicted path of sunlight is one option, but sunlight emerging at the top of the atmosphere will come from many different paths; sunlight reflected by the surface will need to travel back through the same gases (and likely other properties) on its way back to the top of the atmosphere, which is not shown. The spectra in Fig. 1 are generated with SBDART using a set of arbitrary but realistic atmospheric and surface properties.

** SCIAMACHY = Scanning Imaging Absorption Spectrometer for Atmospheric Chartography.

Jake completed his PhD at Reading in 2018 and now works at the NOAA Earth System Research Laboratory (ESRL) in Boulder, Colorado.