## 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

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

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.

## North American weather regimes and the stratospheric polar vortex

The use of weather regimes offers the ability to categorise the large-scale atmospheric circulation pattern over a region on any given day. One way of doing this is through k-means clustering of the 500 hPa geopotential height anomaly field. Cassou (2008) determined the lagged influence of the Madden-Julian Oscillation (MJO) on four wintertime regimes over the North Atlantic; these regimes have subsequently become commonly used (e.g. they are in use operationally at ECMWF). Charlton-Perez et al. (2018) used the same four regimes to describe the influence of the stratospheric polar vortex on Atlantic circulation patterns.

Stratosphere-troposphere coupling is often described in terms of either the annular modes (the leading principal component (PC) of hemisphere-wide variability, often known as the Arctic and Antarctic Oscillations (AO/AAO) when discussing the lower-troposphere) or regional leading principal components (such as the North Atlantic Oscillation (NAO)). However, by their definition, this doesn’t tell the full story – only some percentage of it (around 1/3 for the NAO). The downward coupling of stratospheric circulation anomalies onto tropospheric weather patterns is an area of active research. For example, not every sudden stratospheric warming (SSW) event exhibits the “canonical” response in the troposphere of a strongly negative NAO-type pattern (Karpechko et al. 2017, Domeisen et al. 2020).

Could regimes tell us something more? Specifically – could they shed light onto the impact of the stratosphere on North America, which has been under-explored compared with Europe? In a recent paper (Lee et al. 2019), we look at just that.

We use 500 hPa geopotential height anomalies in the sector 20-80°N 180-30°W from ERA-Interim reanalysis for December—March 1979—2017. In order to describe only the large-scale variability, we first reduced the dimensionality of the problem by performing the clustering on a filtered dataset – achieved by retaining only the first 12 PCs which explain 80% of the variance in the dataset. We set k a priori to be 4 in the ­k-means clustering, following Vigaud et al. (2018). The number of clusters is somewhat arbitrary, but 4 has been shown to be significant when comparing with a reference noise model (i.e., testing if the clusters are just the result of forcefully clustering noise, or something meaningful). Once the clusters have been determined from analysis of the dataset – the “centroids” – each day in the dataset is assigned to one of the clusters. The patterns produced (Figure 1) are like a similar analysis in Straus et al. (2007) so we adopt their names.

To diagnose how these regimes vary with the state of the stratospheric vortex, we compute some statistics (Figure 2) based on the tercile category of the 100 hPa 60°N zonal-mean zonal wind on the preceding day (“strong”, “neutral”, and “weak”). 100 hPa is used as a lower-stratospheric measure (compared with 10 hPa used for diagnosing major sudden stratospheric warmings) to assess only those anomalies in the stratosphere which have the potential to influence tropospheric weather.

Evidently, the Arctic High regime is strongly sensitive to the strength of the stratospheric winds, being 7 times more likely following a weak vortex versus a strong vortex. The Arctic Low regime displays the opposite sensitivity, being more likely following a strong vortex. A similar but weaker relationship is found for the Pacific Trough. The Alaskan Ridge regime, however, does not display a sensitivity to the vortex strength. This result was somewhat surprising as the Alaskan Ridge regime resembles a pattern which became known as a “polar vortex outbreak”, but we suggest that (a) the similarity of the pattern to the Tropical-Northern Hemisphere pattern may indicate tropospheric forcing exhibits greater control on this regime, and (b) a possible influence through a barotropic anomaly exists from a distortion of the stratospheric vortex (which is not manifest in the zonal-mean zonal wind).

We relate these regimes to impactful real-world weather by computing the probability of an extreme cold temperature (defined as 1.5 standard deviations below normal) in each regime (Figure 3). We find that the greatest likelihood of widespread extreme cold in North America is during the Alaskan Ridge regime, with secondary likelihood of extreme cold for the west coast during the Arctic Low (recall that this pattern is more likely following a strong vortex), and only a low probability during the Arctic High regime (which is strongly associated with extreme cold in Europe).

Our results therefore suggest that the strength of the stratospheric polar vortex does not change the likelihood of the circulation pattern with the greatest potential for driving extreme cold weather in North America (in stark contrast to Europe), and that prediction of this pattern should look elsewhere – either to the tropics, or to changes in the shape of the stratospheric vortex – including wave reflection events (Kodera et al. 2008, Kretschmer et al. 2018).

Further work will investigate how well these regimes and their response to changes in the stratosphere are captured by the extended-range forecasting models which comprise the S2S database.

This work was funded by the NERC SCENARIO doctoral training partnership.

## 2019 on The Social Metwork

It’s been quite a busy and successful year here on The Social Metwork, and my first full calendar year as Editor after taking over in October 2018. We’ve had some great contributions on all sorts of topics, from published research to summer schools, conferences, and PhD tips. I’d like to extend my thanks and praise to everyone who has contributed a post or reviewed a submission this year – thank you for taking the time out from your busy PhD life! To those of you who have since finished your PhD, congratulations and all the best for the future. I’d also like to thank everyone who visited the site from around the world (over 5000 of you) and read our blog posts – you’re the reason we do this! – Simon, Editor.

To wrap up 2019, here is a list of all this year’s 32 posts, in case you missed any.

AMS Annual Meeting 2019 – Lewis Blunn

My tips, strategies and hacks as a PhD student – Mark Prosser

Going Part-time… – Rebecca Couchman-Crook

Quantifying the skill of convection-permitting ensemble forecasts for the sea-breeze occurrence – Carlo Cafaro

Is our “ECO mode” hot water boiler eco-friendly? – Mark Prosser

Evaluating aerosol forecasts in London – Elliott Warren

APPLICATE General Assembly and Early Career Science event – Sally Woodhouse

The Circumglobal Teleconnection and its Links to Seasonal Forecast Skill for the European Summer – Jonathan Beverley

Extending the predictability of flood hazard at the global scale – Rebecca Emerton

On relocating to the Met Office for five weeks of my PhD – Kaja Milczewska

Workshop on Predictability, dynamics and applications research using the TIGGE and S2S ensembles – Simon Lee

Representing the organization of convection in climate models – Mark Muetzelfeldt

EGU 2019 – Bethan Harris and Sally Woodhouse

Investigating the use of early satellite data to test historical reconstructions of sea surface temperature – Thomas Hall

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

PhD Visiting Scientist 2019: Prof. Cecilia Blitz – Rebecca Frew

Met Department Summer BBQ 2019 – Mark Prosser

Simulating measurements from the ISMAR radiometer using a new light scattering approximation – Karina McCusker

RMetS Student and Early Career Scientists Conference 2019 – Dom Jones

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

The 27th General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Montreal, Canada – Tsz Yan (Adrian) Leung

The Colour of Climate – Jake Gristey

Fluid Dynamics of Sustainability and the Environment Summer School – Mark Prosser

SWIFT and YESS International Summer School, Kumasi, Ghana – Alex Doyle

Wisdom from experience: advice for new PhD students – Simon Lee and Sally Woodhouse

On relocating to Oklahoma for 3.5 months – Simon Lee

Characterising the seasonal and geographical variability in tropospheric ozone, stratospheric influence and recent changes – Ryan Williams

Combining multiple streams of environmental data into a soil moisture dataset – Amsale Ejigu

How much energy is available in a moist atmosphere? – Bethan Harris

The Variation of Geomagnetic Storm Duration with Intensity – Carl Haines

The impact of atmospheric model resolution on the Arctic – Sally Woodhouse

Sudden Stratospheric Warming does not always equal Sudden Snow Shoveling – Simon Lee

## Sudden Stratospheric Warming does not always equal Sudden Snow Shoveling

During winter, the poles enter permanent darkness (“the polar night”) and undergo strong radiative cooling. In the stratosphere – a dry, stable layer of the atmosphere around 10-50 km above the surface – this cooling is particularly effective. By thermal wind balance, the strong polar cooling leads to the formation of the stratospheric polar vortex (SPV), a planetary scale westerly circulation that sits atop each winter pole (Figure 1).

In the Northern Hemisphere, the SPV is highly variable, thanks to the generation of large planetary waves in the mid-latitude westerly flow (driven primarily by mountains and land-sea contrast around the continents), which can propagate vertically into the stratosphere and break there, decelerating and deforming the SPV and warming the stratosphere.  In the Antarctic, the presence of the Southern Ocean in the mid-to-high latitudes encircling Antarctica means no similar waves are typically produced. The Antarctic SPV is therefore much stronger than its Arctic counterpart, which is why the ozone hole developed there rather than over the Arctic – with the colder temperatures inside the vortex allowing for the formation of polar stratospheric clouds, which catalyse the reactions that deplete ozone.

Now, since all the weather we experience takes place in the troposphere, you might wonder why we should worry about what happens in the layer above that. In the past, numerical weather prediction models did not resolve the stratosphere, because it wasn’t considered worth the extra computational resources. However, it is now known that the state of the SPV can act as a boundary condition to weather forecasts (especially long-range forecasts that extend beyond 2 weeks ahead, e.g. Scaife et al. (2016)) in a similar way to sea surface temperatures (SSTs). One of the reasons for this is the longer timescales present in the stratosphere (also analogous to SSTs) compared with tropospheric weather systems – an anomaly present in the stratosphere has a long persistence time. But how do these stratospheric anomalies influence the weather we experience?

Let’s take one particularly exciting case of SPV variability: major sudden stratospheric warmings (SSWs). SSWs (defined by the 10 hPa 60°N zonal-mean zonal wind reversing from westerlies to easterlies) occur on average 6 times per decade (Butler et al. 2017) and are associated with either a displacement of the SPV off the Pole, or a split of the SPV into two daughter vortices. Coincident with this is a rapid heating of the polar stratosphere (~50°C in a few days) due to adiabatic warming of descending air – hence the name. The most recent major SSW occurred on 2 January 2019 (Figure 2), but one also occurred on 12 February 2018.

Following a major SSW, the easterly winds descend through the stratosphere over the next few weeks and tend to persist for weeks to months in the lower stratosphere. What happens beneath that in the troposphere is then more varied, but on average there is a transition to a negative Northern Annular Mode (NAM). In a negative NAM, the mid-latitude westerlies associated with the tropospheric jet stream weaken and shift equatorward, increasing the likelihood of cold air outbreaks (and, yes, snow!) in places like the UK and northern Europe (Figure 3). However, that’s only the average response!

In February-March 2018, we did indeed see this response following a major SSW – immortalised as the ‘Beast from the East’ with record-breaking cold weather and heavy snowfall in the UK (e.g. Greening and Hodgson 2019). But following the January 2019 SSW, there was no similar weather pattern. Figure 4 shows a cross-section of polar cap geopotential height anomalies (analogous to the NAM). Reds effectively indicate weaker westerly winds, and the major SSW is evident in the centre (second dashed line from the left). However, it doesn’t persistently “drip” down into the troposphere below 200 hPa, with only a brief “drip” in early February 2019. For the most part, the stratosphere and troposphere did not “talk” to each other.

This SSW was thus “non-downward propagating” (Karpechko et al. 2017), which is the case with somewhere close to half of the observed events.

Why?

Some research suggests this may be due to the type of SSW (split vs. displacement, e.g. Mitchell et al. 2013), the tropospheric weather regimes present following the SSW (e.g. Charlton-Perez et al. 2018), the evolution of the SSW (e.g. Karpechko et al. 2017), the interaction of the vertically-propagating waves with the SPV at the time of the SSW (e.g. Kodera et al. 2016), or some combination of those. Perhaps other forcing from the troposphere may dominate over the signal from the stratosphere – such as the teleconnection of the Madden-Julian Oscillation (MJO) to the North Atlantic weather regimes (e.g. Cassou 2008).

Thus, whilst an SSW may make cold weather more likely, it’s by no means guaranteed – and we still don’t fully understand the mechanisms involved with downward coupling. That’s one of the reasons why, regardless of what the tabloids may tell you, sudden stratospheric warming does not always guarantee sudden snow shoveling!

References

Butler, A. H., J. P. Sjoberg, D. J. Seidel, and K. H. Rosenlof, 2017: A sudden stratospheric warming compendium. Earth System Science Data, https://doi.org/10.5194/essd-9-63-2017

Cassou, C., 2008: Intraseasonal interaction between the Madden–Julian Oscillation and the North Atlantic Oscillation. Nature, https://doi.org/10.1038/nature07286

Charlton-Perez, A. J., L. Ferranti, and R. W. Lee, 2018: The influence of the stratospheric state on North Atlantic weather regimes. Quarterly Journal of the Royal Meteorological Society, https://doi.org/10.1002/qj.3280

Greening, K., and A. Hodgson, 2019: Atmospheric analysis of the cold late February and early March 2018 over the UK. Weather, https://doi.org/10.1002/wea.3467

Karpechko, A. Yu., P. Hitchcock, D. H. W. Peters, and A. Schneidereit, 2017: Predictability of downward propagation of major sudden stratospheric warmings. Quarterly Journal of the Royal Meteorological Society, https://doi.org/10.1002/qj.3017

Kodera, K., H. Mukougawa, P. Maury, M. Ueda, and C. Claud, 2016: Absorbing and reflecting sudden stratospheric warming events and their relationship with tropospheric circulation. Journal of Geophysical Research: Atmospheres, https://doi.org/10.1002/2015JD023359

Lee, S. H., and A. H. Butler, 2019: The 2018-2019 Arctic stratospheric polar vortex. Weather, https://doi.org/10.1002/wea.3643

Mitchell, D. M., L. J. Gray, J. Antsey, M. P. Baldwin, and A. J. Charlton-Perez, 2013: The Influence of Stratospheric Vortex Displacements and Splits on Surface Climate. Journal of Climate, https://doi.org/10.1175/JCLI-D-12-00030.1

Scaife, A. A., A. Yu. Karpechko, M. P. Baldwin, A. Brookshaw, A. H. Butler, R. Eade, M. Gordon, C. MacLachlan, N. Martin, N. Dunstone, and D. Smith, 2016: Seasonal winter forecasts and the stratosphere. Atmospheric Science Letters, https://doi.org/10.1002/asl.598

Tripathi, O. P, A. Charlton-Perez, M. Sigmond, and F. Vitart, 2015: Enhanced long-range forecast skill in boreal winter following stratospheric strong vortex conditions. Environmental Research Letters, https://doi.org/10.1088/1748-9326/10/10/104007

## The impact of atmospheric model resolution on the Arctic

The Arctic region is rapidly changing, with surface temperatures warming at around twice the global average and sea ice extent is rapidly declining, particularly in the summer. These changes affect the local ecosystems and people as well as the rest of the global climate. The decline in sea ice has corresponded with cold winters over the Northern Hemisphere mid-latitudes and an increase in other extreme weather events (Cohen et al., 2014). There are many suggested mechanisms linking changes in the sea ice to changes in the stratospheric jet, midlatitude jet and storm tracks; however this is an area of active research, with much ongoing debate.

It is therefore important that we are able to understand and predict the changes in the Arctic, however there is still a lot of uncertainty. Stroeve et al. (2012) calculated time series of September sea ice extent for different CMIP5 models, shown in Figure 1. In general the models do a reasonable job of reproducing the recent trends in sea ice decline, although there is a large inter-model spread and and even larger spread in future projections. One area of model development is increasing the horizontal resolution – where the size of the grid cells used to calculate the model equations is reduced.

The aim of my PhD is to investigate the impact that climate model resolution has on the representation of the Arctic climate. This will help us understand the benefits that we can get from increasing model resolution. The first part of the project was investigating the impact of atmospheric resolution. We looked at three experiments (using HadGEM3-GC2), each at a different atmospheric resolutions: 135km (N512), 60km (N216) and 25km (N96).

The annual mean sea ice concentration for observations and the biases of the 3 experiments are shown in Figure 2. The low resolution experiment does a good job of producing the sea extent seen in observations with only small biases in the marginal sea ice regions. However, in the higher resolution experiments we find that the sea ice concentration is much lower than the observations, particularly in the Barents Sea (north of Norway). These changes in sea ice are consistent with warmer temperatures in the high resolution experiments compared to the low resolution.

To understand where these changes have come from we looked at the energy transported into the ocean by the atmosphere and the ocean. We found that there is an increase in the total energy being transported into the Arctic which is consistent with the reduced sea ice and warmer temperatures. Interestingly, the increase in energy is being transported into the Arctic by the ocean (Figure 3), even though it is the atmospheric resolution that is changing between the experiments. In the high resolution experiments the ocean energy transport into the Arctic, 0.15 petawatts (PW), is in better agreement with observational estimates, 0.154 PW, from Tsubouchi et al. (2018). Interestingly, this is in contrast to the worse representation of sea ice concentration in the high resolution experiments. (It is important to note that the model was tuned at the low resolution and as little as possible was changed when running the high resolution experiments which may contribute to the better sea ice concentration in the low resolution experiment.)

We find that the ocean is very sensitive to the differences in the surface winds between the high and low resolution experiments. In different regions the differences in winds arise from different processes. In the Davis Strait the effect of coastal tiling is important, where at higher resolution a smaller area is covered by atmospheric grid cells that cover both land and ocean. In a cell covering both land and ocean the model usually produces wind speeds to low for over the ocean. Therefore in the higher resolution experiment we find that there are higher wind speeds over the ocean near the coast. Whereas over the Fram Strait and the Barents Sea instead we find that there are large scale atmospheric circulation changes that give the differences in surface winds between the experiments.

References

Cohen, J., Screen, J. A., Furtado, J. C., Barlow, M., Whittleston, D., Coumou, D., Francis, J., Dethloff, K., Entekhabi, D., Overland, J. & Jones, J. 2014: Recent Arctic amplification and extreme mid-latitude weather. Nature Geoscience, 7(9), 627–637, http://dx.doi.org/10.1038/ngeo2234

Stroeve, J. C., Kattsov, V., Barrett, A., Serreze, M., Pavlova, T., Holland, M., & Meier, W. N., 2012: Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophysical Research Letters, 39(16), 1–7, https://doi.org/10.1029/2012GL052676

Tsubouchi, T., Bacon, S., Naveira Garabato, A. C., Aksenov, Y., Laxon, S. W., Fahrbach, E., Beszczynska-Möller, A., Hansen, E., Lee, C.M., Ingvaldsen, R. B. 2018: The Arctic Ocean Seasonal Cycles of Heat and Freshwater Fluxes: Observation-Based Inverse Estimates. Journal of Physical Oceanography, 48(9), 2029–2055, http://journals.ametsoc.org/doi/10.1175/JPO-D-17-0239.1

## The Variation of Geomagnetic Storm Duration with Intensity

Haines, C., M. J. Owens, L. Barnard, M. Lockwood, and A. Ruffenach, 2019: The Variation of Geomagnetic Storm Duration with Intensity. Solar Physics, 294, https://doi.org/10.1007/s11207-019-1546-z

Variability in the near-Earth solar wind conditions can adversely affect a number of ground- and space-based technologies. Some of these space weather impacts on ground infrastructure are expected to increase primarily with geomagnetic storm intensity, but also storm duration, through time-integrated effects. Forecasting storm duration is also necessary for scheduling the resumption of safe operating of affected infrastructure. It is therefore important to understand the degree to which storm intensity and duration are related.

In this study, we use the recently re-calibrated aa index, aaH to analyse the relationship between geomagnetic storm intensity and storm duration over the past 150 years, further adding to our understanding of the climatology of geomagnetic activity. In particular, we construct and test a simple probabilistic forecast of storm duration based on storm intensity.

Using a peak-above-threshold approach to defining storms, we observe that more intense storms do indeed last longer but with a non-linear relationship (Figure 1).

Next, we analysed the distribution of storm durations in eight different classes of storms dependent on the peak intensity of the storm. We found them to be approximately lognormal with parameters depending on the storm intensity. A lognormal distribution is defined by the mean of the logarithm of the values, μ, and the standard deviation of the logarithm of the values, σ. These parameters were found from the observed durations in each intensity class through Maximum Likelihood Estimation (MLE) and used to create a lognormal distribution, plotted in Figure 2 in dark purple. The light purple distribution shows a histogram of the observed data as an estimate of the probability density function (PDF). By eye, the lognormal distribution provides a reasonable first-order match at all intensity thresholds.

On this basis we created a method to probabilistically predict storm duration given peak intensity. For each of the peak intensity classes, we have calculated the values of μ and σ for the lognormal fits to the duration distributions shown as the black points in Figure 3. It is clear from the points in the left panel of Figure 3 that μ increases as intensity increases, agreeing with the previous results in Figure 1 (i.e., duration increases as intensity increases).

The parameter μ can be approximated as a function of storm intensity by:

μ(intensity) = A ln (B intensity−C)

where A, B and C are free parameters. A least squares fit was implemented, and the coefficients A, B and C were found to be 0.455, 4.632, 283.143 respectively and this curve is plotted, along with uncertainty bars, in Figure 3 (left). Although the fit is based on weighted bin-centres of storm intensity, the equation can be used to interpolate for a given value of intensity. σ can be approximated by a linear fit to give σ as a function of the peak intensity. Figure 3 (right) shows the best fit line which has a shallow gradient of −5.08×10−4 and y-intercept at 0.659.

These equations can be used to find lognormal parameters as a function of storm peak intensity. From these, a distribution of duration can be created and hence a probabilistic estimate of the duration of this storm is available. This can be used to predict the probability a storm will last at least e.g. 24 hours. Figure 4 shows the output of the model for a range of storm peak intensity compared against a test set of the aaH index. The model has good agreement with the observations and provides a robust method for estimating geomagnetic storm duration.

The results demonstrate significant advancements in not only understanding the properties and structure of storms, but also how we can predict and forecast these dynamic and hazardous events.

## How much energy is available in a moist atmosphere?

It is often useful to know how much energy is available to generate motion in the atmosphere, for example in storm tracks or tropical cyclones. To this end, Lorenz (1955) developed the theory of Available Potential Energy (APE), which defines the part of the potential energy in the atmosphere that could be converted into kinetic energy.

To calculate the APE of the atmosphere, we first find the minimum total potential energy that could be obtained by adiabatic motion (no heat exchange between parcels of air). The atmospheric setup that gives this minimum is called the reference state. This is illustrated in Figure 1: in the atmosphere on the left, the denser air will move horizontally into the less dense air, but in the reference state on the right, the atmosphere is stable and no motion would occur. No further kinetic energy is expected to be generated once we reach the reference state, and so the APE of the atmosphere is its total potential energy minus the total potential energy of the reference state.

If we think about an atmosphere that only varies in the vertical direction, it is easy to find the reference state if the atmosphere is dry. We assume that the atmosphere consists of a number of air parcels, and then all we have to do is place the parcels in order of increasing potential temperature with height. This ensures that density decreases upwards, so we have a stable atmosphere.

However, if we introduce water vapour into the atmosphere, the situation becomes more complicated. When water vapour condenses, latent heat is released, which increases the temperature of the air, decreasing its density. One moist air parcel can be denser than another at a certain height, but then less dense if they are lifted to a height where the first parcel condenses but the second one does not. The moist reference state therefore depends on the exact method used to sort the parcels by their density.

It is possible to find the rearrangement of the moist air parcels that gives the minimum possible total potential energy, using the Munkres (1957) sorting algorithm, but this takes a very long time for a large number of parcels. Lots of different sorting algorithms have therefore been developed that try to find an approximate moist reference state more quickly (the different types of algorithms are explained by Stansifer (2017) and Harris and Tailleux (2018)). However, these sorting algorithms do not try to analyse whether the parcel movements they are simulating could actually happen in the real atmosphere—for example, many work by lifting all parcels to a fixed level in the atmosphere, without considering whether the parcels could feasibly move there—and there has been little understanding of whether the reference states they find are accurate.

As part of my PhD, I have performed the first assessment of these sorting algorithms across a wide range of atmospheric data, using over 3000 soundings from both tropical island and mid-latitude continental locations (Harris and Tailleux, 2018). This showed that whilst some of the sorting algorithms can provide a good estimate of the minimum potential energy reference state, others are prone to computing a rearrangement that actually has a higher potential energy than the original atmosphere.

We also showed that a new algorithm, which does not rely on sorting procedures, can calculate APE with comparable accuracy to the sorting algorithms. This method finds a layer of near-surface buoyant parcels, and performs the rearrangement by lifting the layer upwards until it is no longer buoyant. The success of this method suggests that we do not need to rely on possibly unphysical sorting algorithms to calculate moist APE, but that we can move towards approaches that consider the physical processes generating motion in a moist atmosphere.

References

Harris, B. L. and R. Tailleux, 2018: Assessment of algorithms for computing moist available potential energy. Q. J. R. Meteorol. Soc., 144, 1501–1510, https://doi.org/10.1002/qj.3297

Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157–167, https://doi.org/10.3402/tellusa.v7i2.8796

Munkres, J., 1957: Algorithms for the Assignment and Transportation Problems. J. Soc. Ind. Appl. Math., 5, 32–38, https://doi.org/10.1137/0105003

Stansifer, E. M., P. A. O’Gorman, and J. I. Holt, 2017: Accurate computation of moist available potential energy with the Munkres algorithm. Q. J. R. Meteorol. Soc., 143, 288–292, https://doi.org/10.1002/qj.2921

## 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

## Characterising the seasonal and geographical variability in tropospheric ozone, stratospheric influence and recent changes

Williams, R. S., Hegglin, M. I., Kerridge, B. J., Jöckel, P., Latter, B. G., and Plummer, D. A.: Characterising the seasonal and geographical variability in tropospheric ozone, stratospheric influence and recent changes, Atmos. Chem. Phys., 19, 3589–3620, https://doi.org/10.5194/acp-19-3589-2019, 2019.

Approximately 90 % of atmospheric ozone (O3) today resides in the stratosphere, which we know as the ozone layer (extending from ~15-35 km), where it plays a critical role in filtering out most of the harmful ultraviolet (UV) rays from the sun. The gradual formation of the ozone layer from around 600 million years ago was key in Earth’s evolutionary history, as it enabled life to flourish on land. Lesser known is the importance of the remaining ~ 10 % of atmospheric ozone, which is found in the troposphere and has implications for air quality, radiative forcing and the oxidation capacity of the troposphere. Whilst ozone is a pollutant at ground level, contributing to an estimated 6 million premature deaths globally per year, it also acts to cleanse the troposphere by breaking down a large number of pollutants, along with some greenhouse gases. Ozone is however a greenhouse gas in itself – where it has a maximum radiative forcing in the upper troposphere. It is an example of a non-well mixed gas, owing to its spatially and temporally highly varying sources and sinks, as well as its relatively short global mean tropospheric lifetime of about 3 weeks.

A major source of tropospheric ozone is the photochemical reactions of emission precursors such as carbon monoxide (CO), nitrogen oxides (NOx) and volatile organic compounds (VOCs), which have both natural and anthropogenic sources, in addition to the natural influx of ozone-rich air from the stratosphere. The magnitude of these two competing influences has been poorly quantified until the recent advent of satellite observations and the development of comprehensive chemistry-climate models (CCMs), which simulate interactive chemistry and are stratospherically well-resolved.

Our study aimed to update and extend the knowledge of a previous key study (Lamarque et al., 1999), that investigated the role of stratosphere-troposphere exchange (STE) on tropospheric ozone, using two contemporary state-of-the-art CCMs (EMAC and CMAM) with stratospheric-tagged ozone tracers as a diagnostic. We first sought to validate the realism of the model ozone estimates with respect to satellite observations from the Ozone Monitoring Instrument (OMI), together with spatially and temporally limited vertical profile information provided from ozonesondes, which we resolved globally on a seasonal basis for the troposphere (1000-450 hPa) (Figure 1).

Whilst we found broad overall agreement with both sets of observations, an overall systematic bias in EMAC of + 2-8 DU (Dobson Units) and regionally and seasonally varying biases in CMAM (± 4 DU) can be seen in the respective difference panels (Figure 1b and 1c). A height-resolved comparison of the models with respect to regionally aggregated ozonesonde observations helped us to understand the origin of these model biases. We showed that apparent closer agreement in CMAM arises due to compensation of a low bias in photochemically produced ozone in the troposphere, resulting from the omission of a group of emission precursors in this model, by excessive smearing of ozone from the lower stratosphere due to an inherent high bias. This smearing is induced when accounting for the satellite observation geometry of OMI, necessary to ensure a direct comparison with vertically well-resolved models, which has limited vertical resolution due to its nadir field of view. The opposite was found to be the case in EMAC, with a high (low) bias in the troposphere (lower stratosphere) relative to ozonesondes. Given the similarity in the emission inventories used in both models, the high bias in this model indicates that excess in situ photochemical production from emission precursors is simulated within the interactive chemistry scheme. These findings emphasise the importance of understanding the origin of such biases, which can help prevent erroneous interpretations of subsequent model-based evaluations.

Noting these model biases, we next exploited the fine scale vertical resolution offered by the CCMs to investigate the regional and seasonal variability of the stratospheric influence. Analysis of the model stratospheric ozone (O3S) tracers revealed large differences in the burden of ozone in the extratropical upper troposphere-lower stratosphere (UTLS) region, with some 50-100 % more ozone in CMAM compared to EMAC. We postulated that CMAM must simulate a stronger lower branch of the Brewer-Dobson Circulation, the meridional stratospheric overturning circulation, since the stratospheric influence is isolated using these simulations. This has implications for the simulated magnitude and distribution of the downward flux of ozone from the stratosphere in each model. Shown in Figure 2 is the zonal-mean monthly evolution of ozone volume mixing ratio (ppbv) from ozonesondes and EMAC over the period 1980-2013 for the upper (350 hPa), middle (500 hPa) and lower (850 hPa) troposphere, together with the EMAC O3S and derived fraction of ozone of stratospheric origin (O3F) (%) evolution.

We found that the ozonesonde evolution closely resembles that of both EMAC and CMAM (not shown) throughout the troposphere. A clear correspondence in the seasonality of ozone is also evident for the EMAC O3S tracer, and in turn the O3F evolution, particularly towards the upper troposphere. Nonetheless, both models imply that over 50 % of near-surface ozone is derived from the stratosphere during wintertime in the extratropics, which is substantially greater than that estimated by Lamarque et al. (1999) (~ 10-20 %), and still considerably higher than more recent studies (~ 30-50 %) (e.g. Banarjee et al., 2016). This indicates that the stratospheric influence may indeed be larger than previously thought and is thus an important consideration when attempting to understand past, present and future trends in tropospheric ozone.

Finally, we analysed height-resolved seasonal changes in both the model O3 and O3S between 1980-89 and 2001-10. The calculated hemispheric springtime (MAM/SON) changes in ozone are shown in Figure 3, and equivalently for O3S in Figure 4, for the upper and middle troposphere (350 and 500 hPa), as well as for the surface model level. A general increase in tropospheric ozone was found worldwide in all seasons, which is maximised overall during spring in both the Northern Hemisphere (~ 4-6 ppbv) and the Southern Hemisphere subtropics (~ 2-6 ppbv), corresponding to a relative increase of about 5-10 %. Respectively, a significant stratospheric contribution to this change of ~ 3-5 ppbv and ~ 1-4 ppbv is estimated using the model O3S tracers (~ 50-80 % of the total change), although with substantial inter-model disagreement over the magnitude and sometimes the sign of the attributable change for any given region or season from the stratosphere.

Although surface ozone changes are dominated by regional changes in precursor emissions between the two periods – the largest, statistically significant increases (> 6 ppbv) being over south-east Asia – the changing influence from the stratosphere were estimated to be up to 1–2 ppbv between the two periods in the Northern Hemisphere, albeit with high regional, seasonal and inter-model variability. In relative terms, the stratosphere can be seen to typically explain 25-30 % of the surface change over regions such as the Himalayas, although locally it may represent the dominant driver (> 50 %) where changes in emission precursors are negligible or even declining due to the enforcement of more stringent air quality regulations over regions such as western Europe and eastern North America in recent years.

To summarise, our paper highlights some of the shortcomings of the EMAC and CMAM CCMs with respect to observations and we emphasise the importance of understanding model bias origins when performing subsequent model-based evaluations. Additionally, our evaluations highlight the necessity of a well-resolved stratosphere in models for quantifying the stratospheric influence on tropospheric ozone. We find evidence that the stratospheric influence may be larger than previously thought, compared with previous model-based studies, which is a highly significant finding for understanding tropospheric ozone trends.

References:
Lamarque, J. F., Hess, P. G. and Tie, X. X.: Three‐dimensional model study of the influence of stratosphere‐troposphere exchange and its distribution on tropospheric chemistry., J. Geophys. Res. Atmos., 104(D21), 26363-26372, https://doi:10.1029/1999JD900762, 1999.

Banerjee, A., Maycock, A. C., Archibald, A. T., Abraham, N. L., Telford, P., Braesicke, P., and Pyle, J. A.: Drivers of changes in stratospheric and tropospheric ozone between year 2000 and 2100., Atmos. Chem. Phys., 16, 2727-2746, https://doi.org/10.5194/acp-16-2727-2016, 2016.