High-resolution Dispersion Modelling in the Convective Boundary Layer

In this blog I will first give an overview of the representation of pollution dispersion in regional air quality models (AQMs). I will then show that when pollution dispersion simulations in the convective boundary layer (CBL) are run at $\mathcal{O}$(100 m) horizontal grid length, interesting dynamics emerge that have significant implications for urban air quality.

Modelling Pollution Dispersion

AQMs are a critical tool in the management of urban air pollution. They can be used for short-term air quality (AQ) forecasts, and in making planning and policy decisions aimed at abating poor AQ. For accurate AQ prediction the representation of vertical dispersion in the urban boundary layer (BL) is key because it controls the transport of pollution away from the surface.

Current regional scale Eulerian AQMs are typically run at $\mathcal{O}$(10 km) horizontal grid length (Baklanov et al., 2014). The UK Met Office’s regional AQM runs at 12 km horizontal grid length (Savage et al., 2013) and its forecasts are used by the Department for Environment Food and Rural Affairs (DEFRA) to provide a daily AQ index across the UK (today’s DEFRA forecast). At such horizontal grid lengths turbulence in the BL is sub-grid.

Regional AQMs and numerical weather prediction (NWP) models typically parametrise vertical dispersion of pollution in the BL using K-theory and sometimes with an additional non-local component so that

$F=-K_z \frac{\partial{c}}{\partial{z}} +N_l$

where $F$ is the flux of pollution, $c$ is the pollution concentration, $K(z)$ is a turbulent diffusion coefficient and $z$ is the height from the ground. $N_l$ is the non-local term which represents vertical turbulent mixing under convective conditions due to buoyant thermals (Lock et al., 2000; Siebesma et al., 2007).

K-theory (i.e. $N_l=0$) parametrisation of turbulent dispersion is consistent mathematically with Fickian diffusion of particles in a fluid. If $K(z)$ is taken as constant and particles are released far from any boundaries (i.e. away from the ground and BL capping inversion), the mean square displacement of pollution particles increases proportional to the time since release. Interestingly, Albert Einstein showed that Brownian motion obeys Fickian diffusion. Therefore, pollution particles in K-theory dispersion parametrisations are analogous to memoryless particles undergoing a random walk.

It is known however that at short timescales after emission pollution particles do have memory. In the CBL, far from undergoing a random trajectory, pollution particles released in the surface layer initially tend to follow the BL scale overturning eddies. They horizontally converge before being transported to near the top of the BL in updrafts. This results in large pollution concentrations in the upper BL and low concentrations near the surface at times on the order of one CBL eddy turnover period since release (Deardorff, 1972; Willis and Deardorff, 1981). This has important implications for ground level pollution concentration predicted by AQMs (as demonstrated later).

Pollution dispersion can be thought of as having two different behaviours at short and long times after release. In the short time “ballistic” limit, particles travel at the velocity within the eddy they were released into, and the mean square displacement of pollution particles increases proportional to the time squared. At times greater than the order of one eddy turnover (i.e. the long time “diffusive” limit) dispersion is less efficient, since particles have lost memory of the initial conditions that they were released into and undergo random motion.  For further discussion of atmospheric diffusion and memory effects see this blog (link).

In regional AQMs, the non-local parametrisation component does not capture the ballistic dynamics and K-theory treats dispersion as being “diffusive”. This means that at CBL eddy turnover timescales it is possible that current AQMs have large errors in their predicted concentrations. However, with increases in computing power it is now possible to run NWP for research purposes at $\mathcal{O}$(100 m) horizontal grid length (e.g. Lean et al., 2019) and routinely at 300 m grid length (Boutle et. al., 2016). At such grid lengths the dominant CBL eddies transporting pollution (and therefore the “ballistic” diffusion) becomes resolved and does not require parametrisation.

To investigate the differences in pollution dispersion and potential benefits that can be expected when AQMs move to $\mathcal{O}$(100 m) horizontal grid length, I have run NWP at horizontal grid lengths ranging from 1.5 km (where CBL dispersion is parametrised) to 55 m (where CBL dispersion is mostly resolved). The simulations are unique in that they are the first at such grid lengths to include a passive ground source of scalar representing pollution, in a domain large enough to let dispersion develop for tens of kilometres downstream.

High-Resolution Modelling Results

A schematic of the Met Office Unified Model nesting suite used to conduct the simulations is shown in Fig. 1. The UKV (1.5 km horizontal grid length) model was run first and used to pass boundary conditions to the 500 m model, and so on down to the 100 m and 55 m models. A puff release, homogeneous, ground source of passive scalar was included in all models and its horizontal extent covered the area of the 55 m (and 100 m) model domains. The puff releases were conducted on the hour, and at the end of each hour scalar concentration was set to zero. The case study date was 05/05/2016 with clear sky convective conditions.

Puff Releases

Figure 2 shows vertical cross-sections of puff released tracer in the UKV and 55 m models at 13-05, 13-20 and 13-55 UTC. At 13-05 UTC the UKV model scalar concentration is very large near the surface and approximately horizontally homogeneous. The 55 m model concentrations however are either much closer to the surface or elevated to great heights within the BL in narrow vertical regions. The heterogeneity in the 55 m model field is due to CBL turbulence being largely resolved in the 55 m model. Shortly after release, most scalar is transported predominantly horizontally rather than vertically, but at localised updrafts scalar is transported rapidly upwards.

By 13-20 UTC it can be seen that the 55 m model has more scalar in the upper BL than lower BL and lowest concentrations within the BL are near the surface. However, the scalar in the UKV model disperses more slowly from the surface. Concentrations remain unrealistically larger in the lower BL than upper BL and are very horizontally homogeneous, since the “ballistic” type dispersion is not represented. By 13-55 UTC the concentration is approximately uniform (or “well mixed”) within the BL in both models and dispersion is tending to the “diffusive” limit.

It has thus been demonstrated that unless “ballistic” type dispersion is represented in AQMs the evolution of the scalar concentration field will exhibit unphysical behaviour. In reality, pollution emissions are usually continuously released rather than puff released. One could therefore ask the question – when pollution is emitted continuously are the detailed dispersion dynamics important for urban air quality or does the dynamics of particles released at different times cancel out on average?

Continuous Releases

To address this question, I included a continuous release, homogeneous, ground source of passive scalar. It was centred on London and had dimensions 50 km by 50 km which is approximately the size of Greater London. Figure 3a shows a schematic of the source.

The ratio of the 55 m model and UKV model zonally averaged surface concentration with downstream distance from the southern edge of the source is plotted in Fig. 3b. The largest difference in surface concentration between the UKV and 55m model occurs 9 km downstream, with a ratio of 0.61. This is consistent with the distance calculated from the average horizontal velocity in the BL ($\approx$7 ms-1) and the time at which there was most scalar in the upper BL compared to the lower BL in the puff release simulations ($\approx$ 20 min). The scalar is lofted high into the BL soon after emission, causing reductions in surface concentrations downstream. Beyond 9 km downstream distance a larger proportion of the scalar in the BL has had time to become well-mixed and the ratio increases.

Summary

By comparing the UKV and 55 m model surface concentrations, it has been demonstrated that “ballistic” type dispersion can influence city scale surface concentrations by up to approximately 40%. It is likely that by either moving to $\mathcal{O}$(100 m) horizontal grid length or developing turbulence parametrisations that represent “ballistic” type dispersion, that substantial improvements in the predictive capability of AQMs can be made.

References

1. Baklanov, A. et al. (2014) Online coupled regional meteorology chemistry models in Europe: Current status and prospects https://doi.org/10.5194/acp-14-317-2014
1. Boutle, I. A. et al. (2016) The London Model: Forecasting fog at 333 m resolution https://doi.org/10.1002/qj.2656
1. Deardorff, J. (1972) Numerical Investigation of Neutral and Unstable Planetary Boundary Layers https://doi.org/10.1175/1520-0469(1972)029<0091:NIONAU>2.0.CO;2
1. DEFRA – air quality forecast https://uk-air.defra.gov.uk/index.php/air-pollution/research/latest/air-pollution/daqi
1. Lean, H. W. et al. (2019) The impact of spin-up and resolution on the representation of a clear convective boundary layer over London in order 100 m grid-length versions of the Met Office Unified Model https://doi.org/10.1002/qj.3519
1. Lock, A. P. et al. A New Boundary Layer Mixing Scheme. Part I: Scheme Description and Single-Column Model Tests https://doi.org/10.1175/1520-0493(2000)128<3187:ANBLMS>2.0.CO;2
1. Savage, N. H. et al. (2013) Air quality modelling using the Met Office Unified Model (AQUM OS24-26): model description and initial evaluation https://doi.org/10.5194/gmd-6-353-2013
1. Siebesma, A. P. et al. (2007) A Combined Eddy-Diffusivity Mass-Flux Approach for the Convective Boundary Layer https://doi.org/10.1175/JAS3888.1
1. Willis. G and J. Deardorff (1981) A laboratory study of dispersion from a source in the middle of the convectively mixed layer https://doi.org/10.1016/0004-6981(81)90001-9

A new, explicit thunderstorm electrification scheme for the Met Office Unified Model

Forecasting lightning is a difficult problem due to the complexity of the lightning process and how dependent the lightning forecast is on the accuracy of the convective forecast. In order to verify forecasts of lightning independently of the accuracy of the convective forecast, it can be helpful to introduce a lightning scheme that is more complex and physically representative than the simple lightning parameterisations often used in Numerical Weather Prediction (NWP).

The existing method of predicting lightning in the Met Office’s Unified Model (MetUM) uses upwards graupel flux and total ice water path, based on the method of McCaul et al. (2009). However, this method tends to overpredict the total number and coverage of lighting, particularly in the UK.

I’ve implemented a physically based, explicit electrification scheme in the MetUM in order to try and improve the current lightning forecasts. The processes involved in the scheme are shown in the flowchart in Figure 1. The electrification scheme uses the Non-Inductive Charging (NIC) process to separate charge within thunderstorms (Mansell et al., 2005; Saunders and Peck, 1998). The NIC theory states that when graupel and ice crystals collide some charge is transferred from one particle to the other. The sign and the magnitude of the charge that is transferred to the graupel particle depends on a number of parameters. It is affected by the ice crystal diameter, the velocity of the collision, the liquid water content and the temperature at which the collision occurs. Once the charge has been generated on graupel and ice or snow particles, it can be moved around the model domain and can be transferred between hydrometeor species. Charge is removed from hydrometeor species and the domain when the hydrometeors precipitate to the surface or if the hydrometeor evaporates or sublimates. Charge is transferred between hydrometeor species proportionally to the mass that is transferred. Charge is held on graupel, rain and cloud ice (or aggregates and crystals if these are included separately).

Once these charged hydrometeors are distributed through the cloud, they can be totalled to create a charge density distribution. From this distribution the electric field can be calculated. Then from the electric field lightning flashes can be discharged. Lightning flashes are discharged based on two thresholds, the first of these is the initiation threshold and governs where the initiation point for the lightning channel should be (Marshall et al., 1995). The second of these is a propagation threshold and governs whether or not the lightning channel can move through a grid box (Barthe et al., 2012). Lightning channels are only allowed to propagate vertically within a grid column to simplify the model structure (Fierro et al., 2013). Once the channel is created charge is neutralised along the channel, charge is removed from hydrometeor species in both the channel and the grid points immediately adjacent to the channel.

The updated charge density distribution is then used to recalculate the electric field and new flashes are discharged from any points that exceed the electric field threshold. This process keeps repeating until no new lightning flashes are discharged within the domain.

The plots in Figure 2 show the charge on graupel (a), cloud ice (b), rain (c) and the total charge (d) for a small single cell thunderstorm in the south of the UK on the 31st August 2017. It can be seen in these figure that the charge is mainly positive on cloud ice and mainly negative on graupel. The cloud ice, being less dense is lofted towards the top of the thunderstorm, while the graupel being denser generally falls towards the bottom of the storm. This creates the charge structure seen in Fig. 2d, with two positive-negative dipoles. This charge structure allows for the development of strong electric fields between the positive and negative charge centres in each dipole. If the electric field between the charge centres reaches the order of 100s kVm-1 the air can become electrically conductive, causing lightning.

The electrification scheme was run within the operational configuration of the MetUM for a case study. The case study was a case of some organised and some single-cell, fair weather convection, on the 31st August 2017. The observations of lightning flashes are taken from the Met Office’s ATDNet lightning location system. The results of the total lighting accumulated for the entire day of the 31st August are shown in Figure 3. It can be easily seen that the existing method is producing far too much lightning compared to the observations. The new scheme is much closer to the observations.

It is an improvement, not only in the total lightning output, but also in the appearance of the lightning flash map. The scattered nature of the observations is captured by the new scheme, whereas the existing parameterisation appears to be largely producing lightning in neat, contoured paths. These paths show that the way that the existing parameterisation predicts lightning is not physically accurate and indicate the problem with the parameterisation, namely that it relies too heavily on the total ice water path. The new scheme suggests a possible improvement, in considering more explicitly the combination of graupel, liquid water and cloud ice that is vital for the production of charge and therefore lightning.

References:
Barthe, C., Chong, M., Pinty, J.-P., and Escobar, J. (2012). CELLS v1.0: updated and parallelized version of an electrical scheme to simulate multiple electrified clouds and flashes over large domains. Geoscientific Model Development, (5), 167–184.

Fierro, A. O., Mansell, E. R., MacGorman, D. R., and Ziegler, C. L. (2013). The Implementation of an Explicit Charging and Discharge Lightning Scheme within the WRF-ARW Model: Benchmark Simulations of a Continental Squall Line, a Tropical Cyclone, and a Winter Storm. Monthly Weather Review, 141, 2390–2415.

Mansell, E. R., MacGorman, D. R., Ziegler, C. L., and Straka, J. M. (2005). Charge structure and lightning sensitivity in a simulated multicell thunderstorm. Journal of Geophysical Research, 110.

Marshall, T. C., McCarthy, M. P., and Rust, W. D. (1995). Electric field magnitudes and lightning initiation in thunderstorms. Journal of Geophysical Research, 100, 7097–7103.

McCaul, E. W., Goodman, S. J., LaCasse, K. M., and Cecil, D. J. (2009). Forecasting lightning threat using cloud-resolving model simulations. Weather and Forecasting, 24(3), 709–729.

Saunders, C. P. R. and Peck, S. L. (1998). Laboratory studies of the influence of the rime accretion rate on charge transfer during crystal / graupel collisions. Journal of Geophysical Research, 103, 949–13.

Island convection and its many shapes and forms: a closer look at cloud trails

Despite decades of research, convection continues to be one of the major sources of uncertainty in weather and climate models. This is because convection occurs across scales that are smaller than the numerical grids used to integrate these models – in other words, the convection is not resolved in the model. However, its role in the vertical transport of heat, moisture, and momentum could still be important for phenomena that are resolved so the impact of convection is estimated from a set of diagnosed parameters (i.e. a parameterisation scheme).

As the community moves toward modelling with smaller numerical grids, convection can be partially resolved. This numerical regime consisting of partially resolved convection is sometimes called the ‘Convection Grey Zone’. New parameterisations for convection are required for the convection grey zone as the underlying assumptions for existing parameterisations are no longer valid.

With smaller grid spacing, other important processes are better represented – for example, the interaction with the surface. In some coarse climate models, many islands are so small that they are neglected altogether. We know that islands regularly force different kinds of convection and so they offer a real-world opportunity to study the kind of locally driven convection that can now be resolved in operational weather models. My thesis aims to take existing research on small islands a step further by considering the problem from the perspective of convection parameterisation.

Bermuda (where I’m from) is a small, relatively flat island located in the western North Atlantic Ocean (e.g. Fig. 1). Cloud trails (CT) here have been unwittingly incorporated into a local legend surrounding an 18th century heist during the American Revolution. This plot to steal British gunpowder to help the American revolutionaries involved the American merchant ‘Captain Morgan’, whose ghost is said to haunt Bermuda on hot, humid summer evenings when dark cloud looms over the east end of the island. This legend is where the local name for the cloud trail “Morgan’s Cloud” comes from (BWS Glossary, 2019).

This story highlights what a CT might look like from a ground observer – a dark cloud which hangs over one end of the island. In fact, CT could only be observed from the ground until research aircraft became feasible in the 1940s and 50s. Aircraft measurements revealed the internal structure of the CT including an associated plume of warmer, drier air immediately downwind of the island.

In the coming decades, the combination of publicly available high-quality satellite imagery and computing advances introduced new avenues for research. This allowed case studies of one-off events and short satellite climatologies constructed by hand (e.g. Nordeen et al., 2001).

Observed from space, CTs look like bands of cloud that stream downwind of, and appear anchored to, small islands. They can be found downwind of small islands around the world, mainly in the tropics and subtropics.

In my thesis, we design an algorithm to automate the objective classification of satellite imagery into one of three categories (Fig. 2): CT, NT (Non-Trail), and OB (Obscured). We find that the algorithm results are comparable to manually classified satellite imagery and can construct a much longer climatology of CT occurrence quickly and objectively (Johnston et al., 2018). The algorithm is applied to satellite imagery of Bermuda for May through October of 2012-2016.

We find that CT occurrence peaks in the afternoon and in July. This highlights the strong link to the solar cycle. Furthermore, radiosonde measurements taken via weather balloon by the Bermuda Weather Service show that cloud base height (which is controlled by the low-level humidity) is too high for NT days. This reduces cloud formation in general and prevents the CT cloud band forming. Meanwhile, large-scale disturbances result in widespread cloud cover on OB days (Johnston et al., 2018).

These observations and measurements can only tell us so much. A case CT day is then used to design numerical experiments to consider poorly observed features of the phenomenon. For example, the interplay between the warm plume, CT circulation, and the clouds themselves. These experiments are completed with very small grid spacing (i.e. 100 m vs. the ~10 km in weather models, and ~50 km in climate models). This allows us to confidently simulate both convection and a small island without the use of parameterisations.

Within the boundary layer which buffers the impacts from surface on the free atmosphere, a circulation forms downwind of the heated island. We show that this circulation consists of near-surface convergence, which leads to a band of ascent, and a region of divergence near the top of the boundary layer. This circulation acts as a coherent structure tying the boundary layer to convection in the free atmosphere above.

Further experiments which target the relationship between the island heating, low-level humidity, and wind speed have been completed. These experiments reveal a range of circulation responses. For instance, responses associated with no cloud, mostly passive cloud, and strongly precipitating cloud can result.

We are now using the set of CT experiments to develop a set of expectations upon which existing and future convection parameterisation schemes can be tested and evaluated. We plan to use a selection of the CT experiments with grid spacing increased to values consistent with current operational grey zone models. We believe that this will help to highlight deficiencies in existing parameterisation schemes and focus efforts for the improvement of future schemes.

Bermuda Weather Service (BWS) Glossary, accessed 2019: Morgan’s Cloud/Morgan’s Cloud (Story). https://www.weather.bm/glossary/glossary.asp

Johnston, M. C., C. E. Holloway, and R. S. Plant, 2018: Cloud Trails Past Bermuda: A Five-Year Climatology from 2012-2016. Mon. Wea. Rev., 146, 4039-4055, https://doi.org/10.1175/MWR-D-18-0141.1

Matthews, S., J. M. Hacker, J. Cole, J. Hare, C. N. Long, and R. M. Reynolds, 2007: Modification of the atmospheric boundary layer by a small island: Observations from Nauru. Mon. Wea. Rev., 135, 891-905, https://doi.org/10.1175/MWR3319.1

Nordeen, M. K., P. Minnis, D. R. Doelling, D. Pethick, and L. Nguyen, 2001: Satellite observations of cloud plumes generated by Nauru. Geophys. Res. Lett., 28, 631-634, https://doi.org/10.1029/2000GL012409

Representing the organization of convection in climate models

Current generation climate models are typically run with horizontal resolutions of 25–50 km. This means that the models cannot explicitly represent atmospheric phenomena that are smaller than these resolutions. An analogy for this is with the resolution of a camera: in a low-resolution, blocky image you cannot make out all the finer details. In the case of climate models, the unresolved phenomena might still be important for what happens at the larger, resolved scales. This is true for convective clouds – clouds such as cumulus and cumulonimbus that are formed from differences in density, caused by latent heat release, between the clouds and the environmental air. Convective clouds are typically around hundreds to thousands of metres in their horizontal size, and so are much smaller than the size of individual grid-columns of a climate model.

Convective clouds are produced by instability in the atmosphere. Air that rises ends up being warmer, and so less dense, than the air that surrounds it, due to the release of latent heat as water is formed by the condensation of water vapour. The heating they produce acts to reduce this instability, leading to a more stable atmosphere. To ensure that this stabilizing effect is included in climate model simulations, convective clouds are represented through what is called a convection parametrization scheme – the stabilization is boiled down to a small number of parameters that model how the clouds act to reduce the instability in a given grid-column. The parametrization scheme then models the action of the clouds in a grid-column by heating the atmosphere higher up, which reduces the instability.

Convection parametrization schemes work by making a series of assumptions about the convective clouds in each grid-column. These include the assumption that there will be many individual convective clouds in grid-columns where convection is active (Fig. 1), and that these clouds will only interact through stabilizing a shared environment. However, in nature, many forms of convective organization are observed, which are not currently represented by convection parametrization schemes.

Figure 1: From Arakawa and Schubert, 1974. Cloud field with many clouds in it – each interacting with each other only by modifying a shared environment.

In my PhD, I am interested in how vertical wind shear can cause the organization of convective cloud fields. Wind shear occurs when the wind is stronger at one height than another. When there is wind shear in the lower part of the atmosphere – the boundary layer – it can organize individual clouds into much larger cloud groups. An example of this is squall lines, which are often seen over the tropics and in mid-latitudes over the USA and China. Squall lines are a type of Mesoscale Convective System (MCS), which account for a large part of the total precipitation over the tropics – between 50 – 80 %. Including their effects in a climate model can therefore have an impact of the distribution of precipitation over the tropics, which is one area where there are substantial discrepancies between climate models and observations.

The goal of my PhD is to work out how to represent shear-induced organization of cloud fields in a climate model’s convection parametrization scheme. The approach I am taking is as follows. First, I need to know where in the climate model the organization of convection is likely to be active. To do this, I have developed a method for examining all of the wind profiles that are produced by the climate model over the tropics, and grouping these into a set of 10 wind profiles that are probably associated with the organization of convection. The link between organization and each grid-column is made by checking that the atmospheric conditions have enough instability to produce convective clouds, and that there is enough low-level shear to make organization likely to happen. With these wind profiles in hand, where they occur can be worked out (Fig. 2 shows the distribution for one of these profiles). The distributions can be compared with distributions of MCSs from satellite observations, and the similarities between the distributions builds confidence that the method is finding wind profiles that are associated with the organization of convection.

Figure 2: Geographical distribution of one of the 10 wind profiles that represents where organization is likely to occur over the tropics. The profile shows a high degree of activity in the north-west tropical Pacific, an area where organization of convection also occurs. This region can be matched to an area of high MCS activity from a satellite derived climatology produced by Mohr and Zipser, 1996.

Second, with these profiles, I can run a set of high-resolution idealized models. The purpose of these is to check that the wind profiles do indeed cause the organization of convection, then to work out a set of relationships that can be used to parametrize the organization that occurs. Given the link between low-level shear and organization, it seems like a good place to start is to check that this link appears in my experiments. Fig. 3 shows the correlation between the low-level shear, and a measure of organization. A clear relationship is seen to hold between these two variables, providing a simple means of parametrizing the degree of organization from the low-level shear in a grid-column.

Figure 3: Correlation of low-level shear (LLS) against a measure of organization (cluster_index). A high degree of correlation is seen, and r-squared values close to 1 indicate that a lot of the variance of cluster_index is explained by the LLS. A p-value of less than 0.001 indicates this is unlikely to have occurred by chance.

Finally, I will need to modify a convection parametrization scheme in light of the relationships that have been uncovered and quantified. To do this, the way that the parametrization scheme models the convective cloud field must be changed to reflect the degree of organization of the clouds. One way this could be done would be by changing the rate at which environmental air mixes into the clouds (the entrainment rate), based on the amount of organization predicted by the new parametrization. From the high-resolution experiments, the strength of the clouds was also seen to be related to the degree of organization, and this implies that a lower value for the entrainment rate should be used when the clouds are organized.

The proof of the pudding is, as they say, in the eating. To check that this change to a parametrization scheme produces sensible changes to the climate model, it will be necessary to make the changes and to run the model. Then the differences in, for example, the distribution of precipitation between the control and the changed climate model can be tested. The hope is then that the precipitation distributions in the changed model will agree more closely with observations of precipitation, and that this will lead to increased confidence that the model is representing more of the aspects of convection that are important for its behaviour.

• Arakawa, A., & Schubert, W. H. (1974). Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. Journal of the Atmospheric Sciences, 31(3), 674-701.
• Mohr, K. I., & Zipser, E. J. (1996). Mesoscale convective systems defined by their 85-GHz ice scattering signature: Size and intensity comparison over tropical oceans and continents. Monthly Weather Review, 124(11), 2417-2437.