## Connecting Global to Local Hydrological Modelling Forecasting – Virtual Workshop

ECMWF- CEMS – C3S – HEPEX – GFP

What was it?

The workshop was organised under the umbrella of ECMWF, the Copernicus services CEMS and C3S, the Hydrological Ensemble Prediction EXperiment (HEPEX) and the Global Flood Partnership (GFP). The workshop lasted 3 days, with a keynote speaker followed by Q&A at the start of each of the 6 sessions. Each keynote talk focused on a different part of the forecast chain, from hybrid hydrological forecasting to the use of forecasts for anticipatory humanitarian action, and how the global and local hydrological scales could be linked. Following this were speedy poster pitches from around the world and poster presentations and discussion in the virtual ECMWF (Gather.town).

Gwyneth – I presented Evaluating the post-processing of the European Flood Awareness System’s medium-range streamflow forecasts in Session 2 – Catchment-scale hydrometeorological forecasting: from short-range to medium-range. My poster showed the results of the recent evaluation of the post-processing method used in the European Flood Awareness System. Post-processing is used to correct errors and account for uncertainties in the forecasts and is a vital component of a flood forecasting system. By comparing the post-processed forecasts with observations, I was able to identify where the forecasts were most improved.

Helen – I presented An evaluation of ensemble forecast flood map spatial skill in Session 3 – Monitoring, modelling and forecasting for flood risk, flash floods, inundation and impact assessments. The ensemble approach to forecasting flooding extent and depth is ideal due to the highly uncertain nature of extreme flooding events. The flood maps are linked directly to probabilistic population impacts to enable timely, targeted release of funding. The Flood Foresight System forecast flood inundation maps are evaluated by comparison with satellite based SAR-derived flood maps so that the spatial skill of the ensemble can be determined.

What did you find most interesting at the workshop?

Gwyneth – All the posters! Every session had a wide range of topics being presented and I really enjoyed talking to people about their work. The keynote talks at the beginning of each session were really interesting and thought-provoking. I especially liked the talk by Dr Wendy Parker about a fitness-for-purpose approach to evaluation which incorporates how the forecasts are used and who is using the forecast into the evaluation.

Helen – Lots! All of the keynote talks were excellent and inspiring. The latest developments in detecting flooding from satellites include processing the data using machine learning algorithms directly onboard, before beaming the flood map back to earth! If openly available and accessible (this came up quite a bit) this will potentially rapidly decrease the time it takes for flood maps to reach both flood risk managers dealing with the incident and for use in improving flood forecasting models.

How was your virtual poster presentation/discussion session?

Gwyneth – It was nerve-racking to give the mini-pitch to +200 people, but the poster session in Gather.town was great! The questions and comments I got were helpful, but it was nice to have conversations on non-research-based topics and to meet some of the EC-HEPEXers (early career members of the Hydrological Ensemble Prediction Experiment). The sessions felt more natural than a lot of the virtual conferences I have been to.

Helen – I really enjoyed choosing my hairdo and outfit for my mini self. I’ve not actually experienced a ‘real’ conference/workshop but compared to other virtual events this felt quite realistic. I really enjoyed the Gather.town setting, especially the duck pond (although the ducks couldn’t swim or quack! J). It was great to have the chance talk about my work and meet a few people, some thought-provoking questions are always useful.

## The effect of surface heat fluxes on the evolution of storms in the North Atlantic storm track

Diabatic processes are typically considered as a source of energy for weather systems and as a primary contributing factor to the maintenance of mid-latitude storm tracks (see Hoskins and Valdes 1990 for some classical reading, but also a more recent reviews, e.g. Chang et al. 2002). However, surface heat exchanges do not necessarily act as a fuel for the evolution of weather systems: the effects of surface heat fluxes and their coupling with lower-tropospheric flow can be detrimental to the potential energy available for systems to grow. Indeed, the magnitude and sign of their effects depend on the different time (e.g., synoptic, seasonal) and length (e.g., global, zonal, local) scales which these effects unfold at.

Heat fluxes arise in response to thermal imbalances which they attempt to neutralise. In the atmosphere, the primary thermal imbalances that are observed correspond with the meridional temperature gradient caused by the equator—poles differential radiative heating from the Sun, and the temperature contrasts at the air—sea interface which essentially derives from the different heat capacities of the oceans and the atmosphere.

In the context of the energetic scheme of the atmosphere, which was first formulated by Lorenz (1955) and commonly known as Lorenz energy cycle, the meridional transport of heat (or dry static energy) is associated with conversion of zonal available potential energy to eddy available potential energy, while diabatic processes at the surface coincide with generation of eddy available potential energy.

The sign of the contribution from surface heat exchanges to the evolution on weather systems is not univocal, as it depends on the specific framework which is used to evaluate their effects. Globally, these have been estimated to have a positive effect on the potential energy budget (Peixoto and Oort, 1992) while locally the picture is less clear, as heating where it is cold and cooling where it is warm would lead to a reduction in temperature variance, which is essentially available potential energy.

The first part of my PhD focussed on assessing the role of local air—sea heat exchanges on the evolution of synoptic systems. To that extent, we built a hybrid framework where the spatial covariance between time anomalies of sensible heat flux F and lower-tropospheric air temperature T  is taken as a measure of the intensity of the air—sea thermal coupling. The time anomalies, denoted by a prime, are defined as departures from a 10-day running mean so that we can concentrate on synoptic variability (Athanasiadis and Ambaum, 2009). The spatial domain where we compute the spatial covariance extends from 30°N to 60°N and from 30°W to 79.5°W, which corresponds with the Gulf Stream extension region, and to focus on air—sea interaction, we excluded grid points covered by land or ice.

This leaves us with a time series for F’—T’ spatial covariance, which we also refer to as FT index.

The FT index is found to be always positive and characterised by frequent bursts of intense activity (or peaks). Composite analysis, shown in Figure 1 for mean sea level pressure (a,d), temperature at 850hPa (b,e) and surface sensible heat flux (c,f), indicates that peaks of the FT index (panels a—c) correspond with intense weather activity in the spatial domain considered (dashed box in Figure 1) while a more settled weather pattern is observed to be typical when the FT index is weak (panels d—f).

We examine the dynamical relationship between the FT index and the area-mean baroclinicity, which is a measure of available potential energy in the spatial domain. To do that, we construct a phase space of FT index and baroclinicity and study the average circulation traced by the time series for the two dynamical variables. The resulting phase portrait is shown in Figure 2. For technical details on phase space analysis refer to Novak et al. (2017), while for more examples of its use see Marcheggiani and Ambaum (2020) or Yano et al. (2020). We observe that, on average, baroclinicity is strongly depleted during events of strong F’—T’ covariance and it recovers primarily when covariance is weak. This points to the idea that events of strong thermal coupling between the surface and the lower troposphere are on average associated with a reduction in baroclinicity, thus acting as a sink of energy in the evolution of storms and, more generally, storm tracks.

Upon investigation of the driving mechanisms that lead to a strong F’—T’ spatial covariance, we find that increases in variances and correlation are equally important and that appears to be a more general feature of heat fluxes in the atmosphere, as more recent results appear to indicate (which is the focus of the second part of my PhD).

In the case of surface heat fluxes, cold sector dynamics play a fundamental role in driving the increase of correlation: when cold air is advected over the ocean surface, flux variance amplifies in response to the stark temperature contrasts at the air—sea interface as the ocean surface temperature field features a higher degree of spatial variability linked to the presence of both the Gulf Stream on the large scale and oceanic eddies on the mesoscale (up to 100 km).

The growing relative importance of the cold sector in the intensification phase of the F’—T’ spatial covariance can also be revealed by looking at the phase portraits for air temperature and cold sector area fraction, which is shown in Figure 3. These phase portraits tell us how these fields vary at different points in the phase space of surface heat flux and air temperature spatial standard deviations (which correspond to the horizontal and vertical axes, respectively). Lower temperatures and larger cold sector area fraction characterise the increase in covariance, while the opposite trend is observed in the decaying stage.

Surface heat fluxes eventually trigger an increase in temperature variance, which within the atmospheric boundary layer follows an almost adiabatic vertical profile which is characteristic of the mixed layer (Stull, 2012).

Stronger surface heat fluxes are associated with a deeper boundary layer reaching higher levels into the troposphere: this could explain the observed increase in correlation as the lower-tropospheric air temperatures become more strongly coupled with the surface, while a lower correlation with the surface ensues when the boundary layer is shallow and surface heat flux are weak. Figure 4 shows a simple diagram summarising the mechanisms described above.

In conclusion, we showed that surface heat fluxes locally can have a damping effect on the evolution of mid-latitude weather systems, as the covariation of surface heat flux and air temperature in the lower troposphere corresponds with a decrease in the available potential energy.

Results indicate that most of this thermodynamically active heat exchange is realised within the cold sector of weather systems, specifically as the atmospheric boundary layer deepens and exerts a deeper influence upon the tropospheric circulation.

## References

• Athanasiadis, P. J. and Ambaum, M. H. P.: Linear Contributions of Different Time Scales to Teleconnectivity, J. Climate, 22, 3720– 3728, 2009.
• Chang, E. K., Lee, S., and Swanson, K. L.: Storm track dynamics, J. Climate, 15, 2163–2183, 2002.
• Hoskins, B. J. and Valdes, P. J.: On the existence of storm-tracks, J. Atmos. Sci., 47, 1854–1864, 1990.
• Lorenz, E. N.: Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167, 1955.
• Marcheggiani, A. and Ambaum, M. H. P.: The role of heat-flux–temperature covariance in the evolution of weather systems, Weather and Climate Dynamics, 1, 701–713, 2020.
• Novak, L., Ambaum, M. H. P., and Tailleux, R.: Marginal stability and predator–prey behaviour within storm tracks, Q. J. Roy. Meteorol. Soc., 143, 1421–1433, 2017.
• Peixoto, J. P. and Oort, A. H.: Physics of climate, American Institute of Physics, New York, NY, USA, 1992.
• Stull, R. B.: Mean boundary layer characteristics, In: An Introduction to Boundary Layer Meteorology, Springer, Dordrecht, Germany, 1–27, 1988.
• Yano, J., Ambaum, M. H. P., Dacre, H., and Manzato, A.: A dynamical—system description of precipitation over the tropics and the midlatitudes, Tellus A: Dynamic Meteorology and Oceanography, 72, 1–17, 2020.

## 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

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 (real) butterfly effect: the impact of resolving the mesoscale range

What does the ‘butterfly effect’ exactly mean? Many people would attribute the butterfly effect to the famous 3-dimensional non-linear model of Lorenz (1963) whose attractor looks like a butterfly when viewed from a particular angle. While it serves as an important foundation to chaos theory (by establishing that 3 dimensions are not only necessary for chaos as mandated in the Poincaré-Bendixson Theorem, but are also sufficient), the term ‘butterfly effect’ was not coined until 1972 (Palmer et al. 2014) based on a scientific presentation that Lorenz gave on a more radical, more recent work (Lorenz 1969) on the predictability barrier in multi-scale fluid systems. In this work, Lorenz demonstrated that under certain conditions, small-scale errors grow faster than large-scale errors in such a way that the predictability horizon cannot be extended beyond an absolute limit by reducing the initial error (unless the initial error is perfectly zero). Such limited predictability, or the butterfly effect as understood in this context, has now become a ‘canon in dynamical meteorology’ (Rotunno and Snyder 2008). Recent studies with advanced numerical weather prediction (NWP) models estimate this predictability horizon to be on the order of 2 to 3 weeks (Buizza and Leutbecher 2015; Judt 2018), in agreement with Lorenz’s original result.

The predictability properties of a fluid system primarily depend on the energy spectrum, whereas the nature of the dynamics per se only plays a secondary role (Rotunno and Snyder 2008). It is well-known that a slope shallower than (equal to or steeper than) -3 in the energy spectrum is associated with limited (unlimited) predictability (Lorenz 1969; Rotunno and Snyder 2008), which could be understood through analysing the characteristics of the energy spectrum of the error field. As shown in Figure 1, the error appears to grow uniformly across scales when predictability is indefinite, and appears to ‘cascade’ upscale when predictability is limited. In the latter case, the error spectra peak at the small scale and the growth rate is faster there.

The Earth’s atmospheric energy spectrum consists of a -3 range in the synoptic scale and a $-\frac{5}{3}$ range in the mesoscale (Nastrom and Gage 1985). While the limited predictability of the atmosphere arises from mesoscale physical processes, it would be of interest to understand how errors grow under this hybrid spectrum, and to what extent do global numerical weather prediction (NWP) models, which are just beginning to resolve the mesoscale $-\frac{5}{3}$ range, demonstrate the fast error growth proper to the limited predictability associated with this range.

We use the Lorenz (1969) model at two different resolutions: $K_{max}=11$, corresponding to a maximal wavenumber of $2^{11}=2048$, and $K_{max}=21$. The former represents the approximate resolution of global NWP models (~ 20 km), and the latter represents a resolution about 1000 times finer so that the shallower mesoscale range is much better resolved. Figure 2 shows the growth of a small-scale, small-amplitude initial error under these model settings.

In the $K_{max}=11$ case where the $-\frac{5}{3}$ range is not so much resolved, the error growth remains more or less up-magnitude, and the upscale cascade is not visible. The error is still much influenced by the synoptic-scale -3 range. Such behaviour largely agrees with the results of a recent study using a full-physics global NWP model (Judt 2018). In contrast, with the higher resolution $K_{max}=21$, the upscale propagation of error in the mesoscale is clearly visible. As the error spreads to the synoptic scale, its growth becomes more up-magnitude.

To understand the dependence of the error growth rate on scales, we use the parametric model of Žagar et al. (2017) by fitting the error-versus-time curve for every wavenumber / scale to the equation $E\left ( t \right )=A\tanh\left ( at+b\right )+B$, so that the parameters $A, B, a$ and $b$ are functions of the wavenumber / scale. Among the parameters, a describes the rate of error growth, the larger the quicker. A dimensional argument suggests that $a \sim (k^3 E(k))^{1/2}$, so that $a$ should be constant for a $-3$ range $(E(k) \sim k^{-3})$, and should grow $10^{2/3}>4.5$-fold for every decade of wavenumbers in the case of a $-\frac{5}{3}$ range. These scalings are indeed observed in the model simulations, except that the sharp increase pertaining to the $-\frac{5}{3}$ range only kicks in at $K \sim 15$ (1 to 2 km), much smaller in scale than the transition between the $-3$ and $-\frac{5}{3}$ ranges at $K \sim 7$ (300 to 600 km). See Figure 3 for details.

This explains the absence of the upscale cascade in the $K_{max}=11$ simulation. As models go into very high resolution in the future, the strong predictability constraints proper to the mesoscale $-\frac{5}{3}$ range will emerge, but only when it is sufficiently resolved. Our idealised study with the Lorenz model shows that this will happen only if $K_{max} >15$. In other words, motions at 1 to 2 km have to be fully resolved in order for error growth in the small scales be correctly represented. This would mean a grid resolution of ~ 250 m after accounting for the need of a dissipation range in a numerical model (Skamarock 2004).

While this seems to be a pessimistic statement, we have observed that the sensitivity of the error growth behaviour to the model resolution is itself sensitive to the initial error profile. The results presented above are for an initial error confined to a single small scale. When the initial error distribution is changed, the qualitative picture of error growth may not present such a contrast between the two resolutions. Thus, we highlight the need of further research to assess the potential gains of resolving more scales in the mesoscale, especially for the case of a realistic distribution of error that initiates the integrations of operational NWP models.

A manuscript on this work has been submitted and is currently under review.

This work is supported by a PhD scholarship awarded by the EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth, with additional funding support from the ERC Advanced Grant ‘Understanding the Atmospheric Circulation Response to Climate Change’ and the Deutsche Forschungsgemeinschaft (DFG) Grant ‘Scaling Cascades in Complex Systems’.

References

Buizza, R. and Leutbecher, M. (2015). The forecast skill horizon. Quart. J. Roy. Meteor. Soc. 141, 3366—3382. https://doi.org/10.1002/qj.2619

Judt, F. (2018). Insights into atmospheric predictability through global convection-permitting model simulations. J. Atmos. Sci. 75, 1477—1497. https://doi.org/10.1175/JAS-D-17-0343.1

Leung, T. Y., Leutbecher, M., Reich, S. and Shepherd, T. G. (2019). Impact of the mesoscale range on error growth and the limits to atmospheric predictability. Submitted.

Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. J. Atmos. Sci. 20, 130—141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

Lorenz, E. N. (1969). The predictability of a flow which possesses many scales of motion. Tellus 21, 289—307. https://doi.org/10.3402/tellusa.v21i3.10086

Nastrom, G. D. and Gage, K. S. (1985). A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci. 42, 950—960. https://doi.org/10.1175/1520-0469(1985)042<0950:ACOAWS>2.0.CO;2

Palmer, T. N., Döring, A. and Seregin, G. (2014). The real butterfly effect. Nonlinearity 27, R123—R141. https://doi.org/10.1088/0951-7715/27/9/R123

Rotunno, R. and Snyder, C. (2008). A generalization of Lorenz’s model for the predictability of flows with many scales of motion. J. Atmos. Sci. 65, 1063—1076. https://doi.org/10.1175/2007JAS2449.1

Skamarock, W. C. (2004). Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev. 132, 3019—3032. https://doi.org/10.1175/MWR2830.1

Žagar, N., Horvat, M., Zaplotnik, Ž. and Magnusson, L. (2017). Scale-dependent estimates of the growth of forecast uncertainties in a global prediction system. Tellus A 69:1, 1287492. https://doi.org/10.1080/16000870.2017.1287492

## Combining multiple streams of environmental data into a soil moisture dataset

An accurate estimate of soil moisture has a vital role in a number of scientific research areas. It is important for day to day numerical weather prediction, extreme weather event forecasting such as for flooding and droughts, crop suitability to a particular region and crop yield estimation to mention a few. However, in-situ measurements of soil moisture are generally expensive to obtain, labour intensive and have sparse spatial coverage. To assist this, satellite measurements and models are used as a proxy of the ground measurement. Satellite missions such as SMAP (Soil Moisture Active Passive) observe the soil moisture content for the top few centimetres from the surface of the earth. On the other hand, soil moisture estimates from models are prone to errors due to model errors in representing the physics or the parameter values used.

Data assimilation is a method of combining numerical models with observed data and its error statistics. In principle, the state estimate after data assimilation is expected to be better than the standalone numerical model estimate of the state or the observations. There are a variety of data assimilation methods: Variational, Sequential, Monte Carlo methods and a combination of them. The Joint UK Land Environment Simulator (JULES) is a community land surface model which calculates several land surface processes such as surface energy balance and carbon cycle and used by the Met Office – the UK’s national weather service.

My PhD aims to improve the estimate of soil moisture from the JULES model using satellite data from SMAP and the Four-Dimensional Ensemble Variational (4DEnVar) data assimilation method introduced by Liu et al. (2008) and implemented by Pinnington (2019; under review), a combination of Variational and Ensemble data assimilation methods. In addition to satellite soil moisture data assimilation, ground measurement soil moisture data from Oklahoma Mesoscale Networks (Mesonet) are also assimilated.

The time series of soil moisture from the JULES model (prior), soil moisture obtained after assimilation (posterior) and observed soil moisture for Antlers station in Mesonet are depicted in Figure 1. Figure 2 shows the distance of prior soil moisture estimates and posterior soil moisture estimates from the assimilated observations. The smaller the distance is the better as the primary objective of data assimilation is to optimally fit the model trajectory into the observations and background. From Figure 1 and Figure 2 we can conclude that posterior soil moisture estimates are closer to the observations compared to the prior. Looking at particular months, prior soil moisture is closer to observations compared to the posterior around January and October. This is due to the fact that 4DEnVar considers all the observations to calculate an optimal trajectory which fits observations and background. Hence, it is not surprising to see the prior being closer to the observations than the posterior in some places.

Data assimilation experiments are repeated for different sites in Mesonet with varying soil type, topography and different climate and with different soil moisture dataset. In all the experiments, we have observed that posterior soil moisture estimates are closer to the observations than the prior soil moisture estimates. As a verification, soil moisture reanalysis is calculated for the year 2018 and compared to the observations. Figure 3 is SMAP soil moisture data assimilated into the JULES model and hind-casted for the following year.

References

Liu, C., Q. Xiao, and B. Wang, 2008: An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test. Mon. Weather Rev., 136 (9), 3363–3373., https://doi.org/10.1175/2008MWR2312.1

Pinnington, E., T. Quaife, A. Lawless, K. Williams, T. Arkebauer, and D. Scoby, 2019: The Land Variational Ensemble Data Assimilation fRamework:
LaVEnDAR. Geosci. Model Dev. Discuss. https://doi.org/10.5194/gmd-2019-60

## APPLICATE General Assembly and Early Career Science event

On 28th January to 1st February I attended the APPLICATE (Advanced Prediction in Polar regions and beyond: modelling, observing system design and LInkages associated with a Changing Arctic climaTE (bold choice)) General Assembly and Early Career Science event at ECMWF in Reading. APPLICATE is one of the EU Horizon 2020 projects with the aim of improving weather and climate prediction in the polar regions. The Arctic is a region of rapid change, with decreases in sea ice extent (Stroeve et al., 2012) and changes to ecosystems (Post et al., 2009). These changes are leading to increased interest in the Arctic for business opportunities such as the opening of shipping routes (Aksenov et al., 2017). There is also a lot of current work being done on the link between changes in the Arctic and mid-latitude weather (Cohen et al., 2014), however there is still much uncertainty. These changes could have large impacts on human life, therefore there needs to be a concerted scientific effort to develop our understanding of Arctic processes and how this links to the mid-latitudes. This is the gap that APPLICATE aims to fill.

The overarching goal of APPLICATE is to develop enhanced predictive capacity for weather and climate in the Arctic and beyond, and to determine the influence of Arctic climate change on Northern Hemisphere mid-latitudes, for the benefit of policy makers, businesses and society.

APPLICATE Goals & Objectives

Attending the General Assembly was a great opportunity to get an insight into how large scientific projects work. The project is made up of different work packages each with a different focus. Within these work packages there are then a set of specific tasks and deliverables spread out throughout the project. At the GA there were a number of breakout sessions where the progress of the working groups was discussed. It was interesting to see how these discussions worked and how issues, such as the delay in CMIP6 experiments, are handled. The General Assembly also allows the different work packages to communicate with each other to plan ahead, and for results to be shared.

One of the big questions APPLICATE is trying to address is the link between Arctic sea-ice and the Northern Hemisphere mid-latitudes. Many of the presentations covered different aspects of this, such as how including Arctic observations in forecasts affects their skill over Eurasia. There were also initial results from some of the Polar Amplification (PA)MIP experiments, a project that APPLICATE has helped coordinate.

At the end of the week there was the Early Career Science Event which consisted of a number of talks on more soft skills. One of the most interesting activities was based around engaging with stakeholders. To try and understand the different needs of a variety of stakeholders in the Arctic (from local communities to shipping companies) we had to try and lobby for different policies on their behalf. This was also a great chance to meet other early career scientists working in the field and get to know each other a bit more.

What a difference a day makes, heavy snow getting the ECMWF’s ducks in the polar spirit.

#### References

Aksenov, Y. et al., 2017. On the future navigability of Arctic sea routes: High-resolution projections of the Arctic Ocean and sea ice. Marine Policy, 75, pp.300–317.

Cohen, J. et al., 2014. Recent Arctic amplification and extreme mid-latitude weather. Nature Geoscience, 7(9), pp.627–637.

Post, E. & Others, 24, 2009. Ecological Dynamics Across the Arctic Associated with Recent Climate Change. Science, 325(September), pp.1355–1358.

Stroeve, J.C. et al., 2012. Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophysical Research Letters, 39(16), pp.1–7.

## Evaluating aerosol forecasts in London

Aerosols in urban areas can greatly impact visibility, radiation budgets and our health (Chen et al., 2015). Aerosols make up the liquid and solid particles in the air that, alongside noxious gases like nitrogen dioxide, are the pollution in cities that we often hear about on the news – breaking safety limits in cities across the globe from London to Beijing. Air quality researchers try to monitor and predict aerosols, to inform local councils so they can plan and reduce local emissions.

Recently, large numbers of LiDARs (Light Detection and Ranging) have been deployed across Europe, and elsewhere – in part to observe aerosols. They effectively shoot beams of light into the atmosphere, which reflect off atmospheric constituents like aerosols. From each beam, many measurements of reflectance are taken very quickly over time – and as light travels further with more time, an entire profile of reflectance can be constructed. As the penetration of light into the atmosphere decreases with distance, the reflected light is usually commonly called attenuated backscatter (β). In urban areas, measurements away from the surface like these are sorely needed (Barlow, 2014), so these instruments could be extremely useful. When it comes to predicting aerosols, numerical weather prediction (NWP) models are increasingly being considered as an option. However, the models themselves are very computationally expensive to run so they tend to only have a simple representation of aerosol. For example, for explicitly resolved aerosol, the Met Office UKV model (1.5 km) just has a dry mass of aerosol [kg kg-1] (Clark et al., 2008). That’s all. It gets transported around by the model dynamics, but any other aerosol characteristics, from size to number, need to be parameterised from the mass, to limit computation costs. However, how do we know if the estimates of aerosol from the model are actually correct? A direct comparison between NWP aerosol and β is not possible because fundamentally, they are different variables – so to bridge the gap, a forward operator is needed.

In my PhD I helped develop such a forward operator (aerFO, Warren et al., 2018). It’s a model that takes aerosol mass (and relative humidity) from NWP model output, and estimates what the attenuated backscatter would be as a result (βm). From this, βm could be directly compared to βo and the NWP aerosol output evaluated (e.g. see if the aerosol is too high or low). The aerFO was also made to be computationally cheap and flexible, so if you had more information than just the mass, the aerFO would be able to use it!

Among the aerFO’s several uses (Warren et al., 2018, n.d.), was the evaluation of NWP model output. Figure 2 shows the aerFO in action with a comparison between βm and observed attenuated backscatter (βo) measured at 905 nm from a ceilometer (a type of LiDAR) on 14th April 2015 at Marylebone Road in London. βm was far too high in the morning on this day. We found that the original scheme the UKV used to parameterise the urban surface effects in London was leading to a persistent cold bias in the morning. The cold bias would lead to a high relative humidity, so consequently the aerFO condensed more water than necessary, onto the aerosol particles as a result, causing them to swell up too much. As a result, bigger particles mean bigger βm and an overestimation. Not only was the relative humidity too high, the boundary layer in the NWP model was developing too late in the day as well. Normally, when the surface warms up enough, convection starts, which acts to mix aerosol up in the boundary layer and dilute it near the surface. However, the cold bias delayed this boundary layer development, so the aerosol concentration near the surface remained high for too long. More mass led to the aerFO parameterising larger sizes and total numbers of particles, so overestimated βm. This cold bias effect was reflected across several cases using the old scheme but was notably smaller for cases using a newer urban surface scheme called MORUSES (Met Office – Reading Urban Surface Exchange Scheme). One of the main aims for MORUSES was to improve the representation of energy transfer in urban areas, and at least to us it seemed like it was doing a better job!

References

Barlow, J.F., 2014. Progress in observing and modelling the urban boundary layer. Urban Clim. 10, 216–240. https://doi.org/10.1016/j.uclim.2014.03.011

Chen, C.H., Chan, C.C., Chen, B.Y., Cheng, T.J., Leon Guo, Y., 2015. Effects of particulate air pollution and ozone on lung function in non-asthmatic children. Environ. Res. 137, 40–48. https://doi.org/10.1016/j.envres.2014.11.021

Clark, P.A., Harcourt, S.A., Macpherson, B., Mathison, C.T., Cusack, S., Naylor, M., 2008. Prediction of visibility and aerosol within the operational Met Office Unified Model. I: Model formulation and variational assimilation. Q. J. R. Meteorol. Soc. 134, 1801–1816. https://doi.org/10.1002/qj.318

Warren, E., Charlton-Perez, C., Kotthaus, S., Lean, H., Ballard, S., Hopkin, E., Grimmond, S., 2018. Evaluation of forward-modelled attenuated backscatter using an urban ceilometer network in London under clear-sky conditions. Atmos. Environ. 191, 532–547. https://doi.org/10.1016/j.atmosenv.2018.04.045

Warren, E., Charlton-Perez, C., Kotthaus, S., Marenco, F., Ryder, C., Johnson, B., Lean, H., Ballard, S., Grimmond, S., n.d. Observed aerosol characteristics to improve forward-modelled attenuated backscatter. Atmos. Environ. Submitted