## Tips for working from home as a PhD student

As PhD students, working from home is an option for many of us on a “normal” day – as indeed is increasingly the case with jobs which primarily need just an Internet connection. But, thanks to COVID-19, working from home (WFH) is our new collective reality. So how can we make this work well, when for many, our offices may only now be a few steps away from our beds? We asked around for advice on this matter from current PhD students.

Remember to take a break every half an hour or so. Go away from the desk!

It can be easy to forget to take a break when you’re “at home”, even if you’re also “at work”, and especially when you’re likely closer to the kettle/food/toilet than you would be otherwise. Get up, move around!

Stick to a regular schedule: when you wake up, go to sleep, work, relax, etc.

This is great advice for doing a PhD in general, but even more pertinent now that our routines have been turned upside down.

Pretend that you “go to and from work”, i.e take a morning and afternoon walk/cycle to mark the start and end of your work day.

A commute can be a great time to wake up in the morning and wind down in the evening. Get creative with what you can (safely, and in accordance with government guidance) do to replace your commute during this time.

Pretend that you go to work by dressing accordingly, it makes the brain active and makes you stronger against the ‘do something else’  or ‘ relax’ mode activated by the comfy at home clothes.

It’s tempting to work wearing pyjamas, but will this help your productivity and mindset? Getting dressed for work can also help to maintain your work-life balance.

Look after your posture. If possible, sit at a desk with a screen at the right height.

Try to follow standard health and safety advice when it comes to working long hours at a desk. If possible, invest time and money in making your home working environment a comfortable and non-straining place to be.

If you can at all help it, don’t work in the room where you sleep. It can cause difficulties sleeping.

This also helps add some breaks and changes in your day, which can help to maintain focus and motivation.

Enjoy the benefits of working from home: take a break to actually cook lunch, get things done around the house. Let yourself appreciate the things that are handy about it as well as the negatives.

Being able to get away from your work and do something like ironing, cooking, baking or cleaning might actually help your productivity and concentration by providing a better break than you might otherwise get in an office. Embrace it!

Schedule social e-contact. Don’t let yourself go more than a day without at least hearing someone’s voice on the phone. Use the opportunity to reconnect with old friends.

In Reading, we’re making extensive use of Microsoft Teams to remain in contact with each other and try to mimic our vibrant work atmosphere.

Do (as long as it’s safe to do so) go for walks, head outside, make sure you do some exercise twice a week.

Luckily, we’ve got some very nice weather this week in most of the UK. But do please adhere to social distancing guidelines when you do go outside.

It can be easy for the lines between work and life outside of work to be blurred during a PhD at the best of times, and WFH can make this more problematic. Set your hours, and stick to it.

If you work 8-4, work 8-4! At 4pm, switch your computer off and do something different. Without an evening commute, it can be trickier to bring an end to your working day, but this is probably one of the most important things to maintain.

Most operating systems, including Windows 10, support multiple virtual desktops. Try using one of those for your virtual “work” PC, and another as your virtual “home” PC. Then you can keep the two segregated.

At the end of the day you can switch to your “home” desktop, and then return to “work” the following day.

This Twitter thread has some great advice: https://twitter.com/ProfAishaAhmad/status/1240284544667996163?s=19

Twitter is of course full of great (and not so great) advice. It can keep people connected but also increase anxiety. Be cautious with it, along with all social media during this time.

Allow yourself ample time to adjust, get the important things in order first (friends/family/food/fitness), and build a regular schedule.

This is a huge change. It’s not just a huge change to work, it’s a huge change to our entire lives. Go easy on yourself as you get into the swing of things.

Fill the space around you with plants – it’ll make you feel like you’re outside if you don’t have that luxury – and open your windows every morning (you’ll appreciate the fresh air!)

Nature is very calming. Open the window, listen to the birds (you might hear them more than you used to nowadays).

Extending our best wishes to all from everyone in Reading Meteorology during this challenging time.

## Relationships in errors between meteorological forecasts and air quality forecasts

Email: K.M.Milczewska@pgr.reading.ac.uk

Exposure to pollutants in the air we breathe may trigger respiratory problems. Pollutants such as ozone ($O_{3}$) and particulate matter (PM$_{2.5}$) – particles of about 1/20th of the width of a hair strand – can get into our lungs and cause inflammation, alter their function, or otherwise cause trouble for the cardiovascular system – especially in people with existing underlying respiratory conditions. Although high pollution episodes in the UK are infrequent, the public becomes aware of the associated problems during events such as red skies, in part caused by long-range transport of Saharan dust. Furthermore, the World Health Organisation (WHO) estimates that 85% of UK towns regularly exceed the safe annual PM$_{2.5}$ limit. It is therefore important to forecast surface pollution concentrations accurately in order to enable the public to mitigate some of those adverse health risks.

In general, air pollution can be difficult to forecast near the surface because of the multitude of factors which affect it. Incorrectly modelling chemical processes within the atmosphere, surface emissions or indeed the meteorology can lead to errors in predicting ground-level pollution concentrations. It is well accepted within the literature that weather forecasting is of decisive importance for air quality. Thus, my PhD project tries to link forecast errors in meteorological processes within the atmospheric boundary layer (BL) with forecast errors in pollutants such as $O_{3}$ and $NO_{2}$ (nitrogen dioxide) using the operational air quality forecasting model in the UK, the Air Quality in the Unified Model (AQUM). This model produces an hourly air quality forecast issued to the public by DEFRA in the form of a Daily Air Quality Index (DAQI) and is verified against surface-based observations from the Automatic Urban and Rural Network (AURN).

A three-month evaluation of hourly forecasts from AQUM shows a delay in the average increase of the morning $O_{3}$ + $NO_{2}$ (‘total oxidant’) concentrations when compared to AURN observations. We also know that BL depth is important for the mixing of pollutants – it acts as a sort of lid on top of the lower part of the troposphere. Since the noted lag in total oxidant increase in our model occurs exactly at the time of the morning BL development, we can form a testable hypothesis: that an inaccurate representation of BL processes – specifically, morning BL growth – leads to a delay in entrainment of $O_{3}$-rich air masses from the layer of air above it: the residual layer. It has been suggested in the literature that when the daytime convective mixed layer collapses upon sunset, the remaining pollutants are effectively trapped in the leftover (‘residual’) layer, and thus can act as a night-time reservoir of $O_{3}$ above the stable or neutral night-time boundary layer (NBL).

To test the hypothesis, semi-idealised experiments are conducted. We simulate a one-month long release of chemically inert tracers within the Numerical Atmospheric Dispersion Environment (NAME) using different sets of numerical weather prediction (NWP) outputs. This enables a process-based evaluation of how different meteorology affects tracers within the BL. Tracers are released within the lateral boundaries of the domain centred on the UK. The idea is to separate the effects of meteorology from chemistry on the tracer concentrations. In particular, we want to understand the role of entrainment of $O_{3}$-rich air masses from the residual layer down into the developing BL during the morning hours.

We located around 50 AURN sites in urban locations and compared hourly BL depths from June 2017 in the two sets of NWP output used for the tracer simulations: the UKV and UM Global (UMG) configurations of the Met Office Unified Model. It was found that although the average diurnal profiles of BL depth were quite similar, there was a lag in the morning increase of BL depth within the UMG configuration. This may be because the representation of surface sensible heat flux (SSHF) differs in the two NWP models: the UMG uses a single tile scheme to represent urban areas, whereas the UKV uses a more realistic, two-tile scheme (‘MORUSES’) which distinguishes between roof surfaces and street canyons. SSHF is a measure of energy exchange at the ground, where positive fluxes represent a loss of heat from the surface to the atmosphere. Therefore, a more realistic representation of SSHF results in the UKV being better at capturing and storing urban heat. This leads to a faster development of the BL depth in the UKV compared to the UMG, which in turn could mean that there is more turbulent motion and mixing within the atmosphere.

Assuming that the vertical gradient in pollutant concentrations is positive between the morning BL and the free troposphere, mixing air from above should enhance pollutant concentrations nearer to the surface. Our tracer results show that during days when synoptic conditions are dominated by high pressure, the diurnal cycle in forecast and observed surface pollutant concentrations can be adequately replicated by our simplified set-up. Differences between the diurnal cycle between tracer simulations with the two different meteorological set-ups show that the UKV is not only entraining more tracer from above the boundary layer than the simulation using UMG, but also the concentrations increase on average 1 – 2 hours earlier in the morning. These results suggest that indeed the model meteorology – in particular, representation of BL processes – is important to entrainment of polluted air masses into the BL, which in turn has a significant influence on the surface pollutant concentrations.

Within the past two decades, it has been recognised by the weather and air quality modelling communities that neither type of model can truly exist without the other. This post has discussed just one aspect of how meteorology influences the air quality forecast – there are, of course, many other parameters (e.g. wind speed, precipitation, relative humidity) which affect the forecast pollutant concentrations. We therefore also evaluated night-time errors in the wind speed and found that these errors are positively correlated with the total oxidant forecast errors. This means that when the wind speed forecast is overestimated, it is likely to affect the night-time and morning forecast of both $O_{3}$ and $NO_{2}$ in a significant way.

References

Ambient Air Pollution: A global assessment of exposure and burden of disease. WHO, 2016.

Bohnenstengel S., Evans S., Clark P., Belcher S.: Simulations of the London urban heat island, Quarterly Journal of the Royal Meteorological Society, 2011 vol: 137 (659) pp: 1625-1640

Cocks A., 1993: The Chemistry and Deposition of Nitrogen Species in the Troposphere, The Royal Society of Chemistry, Cambridge 1993

Savage N., Agnew P., Davis L., Ordonez C., Thorpe R., Johnson C., O’Connor F., Dalvi M.: Air quality modelling using the Met Office Unified Model (AQUM OS24-26): model description and initial evaluation, Geoscientific Model Development, 2013 vol: 6 pp: 353-372

Sun J., Mahrt L., Banta R., Pichugina Y.: Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99, Journal of the Atmospheric Sciences, 2012 vol: 69 (1) pp: 338-351

Zhang, 2008: Online-coupled meteorology and chemistry models: History, current status, and outlook. Atmos. Chem. Phys, 2008 vol: 8 (11) pp: 2895-2932

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

Email: Benjamin.Courtier@pgr.reading.ac.uk

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.

## An inter-comparison of Arctic synoptic scale storms between four global reanalysis datasets

Email: alexander.vessey@pgr.reading.ac.uk

The Arctic has changed a lot over the last four decades. Arctic September sea ice extent has decreased rapidly from 1980-present by approximately 3.4 million square-kilometres (see Figure 1). This has made the Arctic more accessible for human activities such as shipping, oil exploration and tourism. As Arctic sea ice is expected to continue to decline in the future, human activity in the Arctic is expected to continue to increase. This will increase the exposure to hazardous weather conditions, such as high winds and high waves, which are associated with Arctic storms. However, the characteristics of Arctic storms are currently not well understood.

One way to investigate current Arctic storm characteristics is to analyse storms in global reanalysis datasets. Reanalysis datasets combine past observations with current weather models to produce spatially and temporally homogeneous datasets, that contain atmospheric data at grid-points around the world at constant time intervals (typically every 6-hours) per day from 1979-present (for the modern, satellite-era reanalyses). Typically, a storm tracking algorithm is used to efficiently process all of the 6-hour data in the reanalysis datasets from 1979 (60,088 time steps!) to identify all of the storms that may have occurred in the past. Storms can be identified in the mean sea level pressure (MSLP) field (as low pressure systems), or in the relative vorticity field (as large rotating systems). The relative vorticity field at 850 hPa (higher in the atmosphere than the atmospheric boundary layer) is typically used so that the field is less influenced by boundary layer processes that may produce areas of high relative vorticity.

At the moment, atmospheric scientists are spoilt for choice when it comes to choosing a reanalysis dataset to analyse. There are reanalysis datasets from multiple institutions; the European Centre for Medium Range Weather Forecasts (ECMWF), the Japanese Meteorological Agency (JMA), the National Aeronautics and Space Administration (NASA), and the National Centers for Environmental Prediction (NCEP). Each institution has created their reanalysis dataset in a slightly different way, by using their own numerical weather prediction model and data assimilation systems. Atmospheric scientists also have to choose whether to use the MSLP field or 850 hPa relative vorticity field when applying their storm tracking algorithm to the reanalysis datasets.

In my recent paper, I aimed to assess Arctic storm characteristics in the multiple reanalysis datasets currently available (ERA-Interim, JRA-55, MERRA-2 and NCEP-CFSR), using a storm tracking algorithm based on 850 hPa relative vorticity and MSLP fields. Below is a short summary of some of the results from the paper.

Despite the Arctic environment changing dramatically over the last four decades, we find that there has been no change in the frequency and intensity of Arctic storms in all the reanalysis datasets compared in this study. It was found in preceding, older versions of atmospheric reanalysis datasets that Arctic storm frequency had increased from 1949-2002 (Walsh. 2008 and Sepp & Jaagus. 2011). This is in contrast with results from the modern reanalysis datasets (from this study, and Simmonds et al. 2008, Serreze and Barrett. 2008 and Zahn et al. 2018) which show no increase in Arctic storm frequency.

Across all the reanalysis datasets, some robust characteristics of Arctic storms were found. For example, the spatial distribution of Arctic storms is found to be seasonally dependent. In winter (DJF), Arctic storm track density is highest over the Greenland, Norwegian and Barents Seas, whereas in summer (JJA), Arctic storm track density is highest over and north of the Eurasia coastline (a region known as the Arctic Frontal Zone (Reed & Kunkel. 1960)) (see Figure 2). The number of trans-Arctic ships in summer is much higher than in winter, and these ships typically use the Northern Sea Route to travel between Europe and Asia (along the coastline of Eurasia). Figure 2b shows that this in fact is where most of the summer Arctic storms occur. In addition, the reanalysis datasets show that ~50% of Arctic storms have genesis in mid-latitude regions (south of 65°N) and travel northwards into the Arctic (north of 65°N). This shows that storms are a significant mechanism for transporting air from low to high latitudes.

In general, there is less consistency in Arctic storm characteristics in winter than in summer. This may be because in winter, the occurrence of meteorological conditions such as low level cloud, stable boundary layers and polar night that are more frequent, which are more challenging to represent in numerical weather prediction models, and for the creation of reanalysis datasets. In addition, there is a low density of conventional observations in winter, and difficulties in identifying cloud and estimating emissivity over snow and ice limit the current use of infrared and microwave satellite data in the troposphere (Jung et al. 2016).

The differences between the reanalysis datasets in Arctic storm frequency per season in winter (DJF) and summer (JJA) (1980-2017) were found to be less than 6 storms per season. On the other hand, the differences in Arctic storm frequency per season between storms identified by a storm tracking algorithm based on 850 hPa relative vorticity and MSLP were found to be 55 storms per season in winter, and 33 storms per season in summer. This shows that the decision to use 850 hPa relative vorticity or MSLP for storm tracking can be more important that the choice of reanalysis dataset.

References:

National Snow & Ice Data Centre (2019) Sea ice index. https://nsidc.org. Accessed 4 Mar 2019.

Reed RJ, Kunkel BA (1960) The Arctic circulation in summer. J. Meteorol. 17(5):489–506.

Sepp M, Jaagus J (2011) Changes in the activity and tracks of Arctic cyclones. Clim. Change 105(3–4):577–595.

Simmonds I, Burke C, Keay K (2008) Arctic climate change as manifest in cyclone behavior. J. Clim. 21(22):5777–5796.

Serreze MC, Barrett AP (2008) The summer cyclone maximum over the central Arctic Ocean. J. Clim. 21(5):1048–1065.

Vessey, A.F., Hodges, K.I., Shaffrey, L.C., Day, J.J., (2020) An inter‑comparison of Arctic synoptic scale storms between four global reanalysis datasets. Clim. Dyn., https://doi.org/10.1007/s00382-020-05142-4

Walsh, J.E., Bromwich, D.H., Overland, J.E., Serreze, M.C. and Wood, K.R., 2018. 100 years of progress in polar meteorology. Meteorological Monographs, 59, pp.21-1.

Zahn M, Akperov M, Rinke A, Feser F, Mokhov I I (2018) Trends of cyclone characteristics in the Arctic and their patterns from different reanalysis data. J. Geophys. Res. Atmos., 123(5):2737–2751.

## Life on Industrial Placement

Email: holly.turner@reading.ac.uk

I finished my PhD last year, and since the start of this year I’ve been doing something rather different. Courtesy of SCENARIO DTP funding, I am doing a 3-month post-doc placement with JBA Consulting in Skipton, North Yorkshire. After spending 3.5 years researching in an academic setting, it is great to be able to apply my knowledge to real-world problems.

Working in industry has a very different feel to working in academia. The science being done has an immediate purpose for the company, rather than being done purely to extend knowledge. In the case of my placement, the work that I am doing is ultimately to benefit the end users of the product.

The field that I am now working in is rather far removed from my PhD project: I have gone from gravity waves to surface water flooding. Whilst it has been quite a steep learning curve to bring myself up to speed with the current science in this area, it is great to branch out. I would urge anyone interested in doing an industrial placement not to be put off by going outside of your subject area. You might find something else that suits you better. It might even be the best step you ever make.

The choosing and setting up of the placement has all been fairly easy for me. SCENARIO had a range of placements available and I chose the one that most interested me. I had to send an application to the company, who then called me for an interview. Once they decided to offer me the placement, SCENARIO did the setting up with both JBA and the university. All I needed to worry about was finding accommodation for the 3 months.

To anyone considering doing an industrial placement: do it! I am currently 3 weeks in and have really enjoyed it so far. Everybody has been welcoming and helpful. I felt like part of the team by the end of my first day.

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

Email: tsz.leung@pgr.reading.ac.uk

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

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## Evaluating ocean eddies in coupled climate simulations on a global scale

Email: s.moreton@pgr.reading.ac.uk

Despite being only between ~10-100 km in spatial scale, mesoscale ocean eddies are important for their role in global heat transport, responding to climate change as well as fluxing heat, momentum and freshwater between the ocean and overlying atmosphere.

As climate models move towards higher resolution, their ocean components are now able to begin to resolve mesoscale eddies. A high resolution ocean is typically defined as ‘eddy-present’ (EP, ¼ degree) where some eddies are permitted at low- to mid- latitudes, or ‘eddy-rich’ (ER, 1/12 degree) where eddies are presented at most latitudes, excluding the Arctic basin and the continental shelf around Antarctica. The benefits of the increased computational expense, associated with running global climate models with a high-resolution ocean, need to be clearly identified [Hewitt et al., 2017]. Many modelling centres have not yet developed an operational version of their climate models with a high resolution ocean component. The benefits of an EP resolution ocean (where some, but not all, eddies are resolved) is not necessarily superior to a coarser resolution ocean with full eddy parameterization.

As part of my PhD, we present the first global assessment of mesoscale surface eddy properties (e.g. distribution, size, speed and lifetime) in two versions of a high-resolution coupled model, with either an EP or an ER resolution ocean. The model results are validated against a gridded satellite altimeter dataset (called AVISO) with a resolution of ¼ degree [Ducet et al., 2000]. We identify and track closed coherent mesoscale eddies, which are defined by their sea surface height (SSH) contours, each day over a 20-year period . Our tracking algorithm is based on Chelton et al. [2011] and Mason et al. [2014]. Our two immediate questions are: how does the representation of mesoscale eddies change between EP and ER resolution? And how do these properties compare to observations and theoretical predictions?

For a full description and evaluation of the results the reader is referred to Moreton et al. [2020], instead key results are highlighted as following:

• Relative to EP, ER resolution simulates more (+60%) and longer-lasting (+23%) eddies, in better agreement with observations. This is shown in the probability density function and zonal average of eddy lifetime for each dataset in figure 1, as well as in the maps of eddy genesis in Figure 2. Both model resolutions represent eddies at the Western Boundary Currents (WBCs) and in the Southern Ocean well, however both fail to capture as many eddies in subtropical gyre interiors, as found in observations. This reflects model biases at the Eastern Boundary Upwelling Systems, and at the Indonesian outflow.
• Eddies are not expected to be able to be resolved when model grid spacing is larger than the Rossby radius of deformation (i.e. at high latitudes as the model grid spacing converges towards the poles ) [Hallberg et al., 2013]. Interestingly, EP resolution does allow for some eddy growth in these regions, although admittedly less than in ER resolution and observations, as shown in the eddy genesis maps in Figure 2.
• A particularly striking outcome of our analysis was the large differences in eddy size across the two resolutions and in observations, as demonstrated by the probability density functions in Figure 3. Note in the figure a speed-based radius is shown (Lspd): a radius typically used to define eddy size [Chelton et al., 2011]. As expected, small eddies in the finer ER resolution are able to be resolved, but interestingly less larger eddies are represented, in comparison to EP resolution and observations. In addition, the increased eddy size in observations compared to EP resolution is noteworthy, despite both having the same apparent resolution of ¼ degree. It is likely observed eddy radii are biased high by the post-processing and interpolation in the creation of the gridded satellite dataset. Caution is advised when using observational eddies, for example in developing eddy parameterization and understanding eddy dynamics.

This work lays the foundation to explore the role of these tracked eddies in mesoscale air-sea coupling within the climate system, something I am currently working on [Moreton et al., in prep].

This work is funded by the NERC CASE studentship with the Met Office, UK.

References:

D. B. Chelton, M. G. Schlax, and R. M. Samelson. Global observations of nonlinear mesoscale eddies. Progress in Oceanography, 91:167 – 216, 2011, https://doi.org/10.1016/j.pocean.2011.01.002

N. Ducet, P. Y. Le Traon, and G. Reverdin. Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and -2. Journal of Geophysical Research: Oceans, 105(C8):19477–19498, 2000, https://doi.org/10.1029/2000JC900063

R. Hallberg. Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects. Ocean Modelling, 72:92–103, 2013, https://doi.org/10.1016/j.ocemod.2013.08.007

H. T. Hewitt, M. J. Bell, E. P. Chassignet, A. Czaja, D. Ferreira, S. M. Griffies, P. Hyder, J. L. McClean, A. L. New, and M. J. Roberts. Will high-resolution global ocean models benefit coupled predictions on short-range to climate timescales? Ocean Modelling, 120, 120-136, 2017, https://doi.org/10.1016/j.ocemod.2017.11.002

E. Mason, A. Pascual, and J. C. McWilliams. A new sea surface height-based code for oceanic mesoscale eddy tracking. Journal of Atmospheric and Oceanic Technology, 31(5):1181–1188, 2014, https://doi.org/10.1175/JTECH-D-14-00019.1

S. Moreton, D. Ferreira, M. Roberts and H. Hewitt. Evaluating surface eddy properties in coupled climate simulations with ‘eddy-present’ and ‘eddy-rich’ ocean resolution. Ocean Modelling, 2020, https://doi.org/10.1016/j.ocemod.2020.101567

S. Moreton, D. Ferreira, M. Roberts and H. Hewitt. SST air-sea heat flux feedback over mesoscale eddies in coupled climate models, in prep.