The Scandinavia-Greenland Pattern: something to look out for this winter

Simon Lee, s.h.lee@pgr.reading.ac.uk

The February-March 2018 European cold-wave, known widely as “The Beast from the East” occurred around 2 weeks after a major sudden stratospheric warming (SSW) event on February 12th. Major SSWs typically occur once every other winter, involving significant disruption to the stratospheric polar vortex (a planetary-scale cyclone which resides over the pole in winter). SSWs are important because their occurrence can influence the type and predictability of surface weather on longer timescales of between 2 weeks to 2 months. This is known as subseasonal-to-seasonal (S2S) predictability, and “bridges the gap” between typical weather forecasts and seasonal forecasts (Figure 1).  

Figure 1: Schematic of medium-range, S2S and seasonal forecasts and their relative skill. [Figure 1 in White et al. (2017)] 

In general, S2S forecasts suffer from relatively low skill. While medium-range forecasts are an initial value problem (depending largely on the initial conditions of the forecast) and seasonal forecasts are a boundary value problem (depending on slowly-varying constraints to the predictions, such as the El Niño-Southern Oscillation), S2S forecasts lie somewhere between the two. However, certain “windows of opportunity” can occur that have the potential to increase S2S skill – and a major SSW is one of them. Skilful S2S forecasts can be of particular benefit to public health planners, the transport sector, and energy demand management, among many others.  

Following an SSW, the eddy-driven jet stream tends to weaken and shift equatorward. This is characteristic of the negative North Atlantic Oscillation (NAO) and negative Arctic Oscillation (AO), and during these patterns the risk of cold air outbreaks significantly increases in places like northwest Europe. So, by knowing this, S2S forecasts issued during the major SSW were able to highlight the increased risk of severely cold weather.  

Given that we know that following an SSW certain weather types are more likely for several weeks, and forecasts may be more skilful, it might seem advantageous to know an SSW was coming at a long lead-time in order to really push the boundaries of S2S prediction. So, what about in 2018?  

In the first paper from my PhD, published in July 2019 in JGR-Atmospheres, we explored the onset of predictions of the February 2018 SSW. We found that, until about 12 days beforehand, extended-range forecasts that contribute to the S2S database (an international collaboration of extended-range forecast data) did not accurately predict the event; in fact, most predictions indicated the vortex would remain unusually strong! 

We diagnosed that anticyclonic wave breaking in the North Atlantic was a crucial synoptic-scale “trigger” event for perturbing the stratospheric vortex, by enhancing vertically propagating Rossby waves (which weaken the vortex when they break in the stratosphere). Forecasts struggled to predict this event far in advance, and thus struggled to predict the SSW. We called the pattern the “Scandinavia-Greenland (S-G) dipole” – characterised by an anticyclone over Scandinavia and a low over Greenland (Figure 2), and we found it was present before 35% of previous SSWs (1979-2018). The result agrees with several previous studies highlighting the role of blocking in the Scandinavia-Urals region, but was the first to suggest such a significant impact of a single tropospheric event.  

Figure 2: Correlation between mean sea level pressure forecasts over 3-5 February 2018 and subsequent forecasts of 10 hPa 60°N zonal-mean zonal wind on 9-11 February, in (a) NCEP and (b) ECMWF ensembles launched between 29 January and 1 February 2018. White lines (dashed negative) indicate correlations exceeding +/- 0.7, while the black dashed lines indicate the nodes of the S-G dipole. [Figure 3 in Lee et al. (2019)] 

So, we had established the S-G dipole was important in the predictability onset in 2018, and important in previous cases – but how well do S2S models generally capture the pattern?  

That was the subject of our recent (open-access) paper, published in August in QJRMS. We define a more generalised pattern by performing empirical orthogonal function (EOF) analysis on mean sea-level pressure anomalies in a region of the northeast Atlantic during November-March in ERA5 reanalysis (Figure 3).  While the leading EOF (the “zonal pattern”) resembles the NAO, the 2nd EOF resembles the S-G dipole from our previous paper – so we call it the “S-G pattern”.  

Figure 3: The first two leading EOFs of MSLP anomalies in the northeast Atlantic during November-March in ERA5, expressed as hPa per standard deviation of the principal component timeseries. The percentage of variance explained by the EOF is also shown. [Figure 1 in Lee et al. (2020) 

We then establish, through lagged linear regression analysis, that the S-G pattern is associated with enhanced vertically propagating wave activity (measured by zonal-mean eddy heat flux) into the stratosphere, and a subsequently weakened stratospheric vortex for the next 2 months. Thus, it supports our earlier work, and motivates considering how the pattern is represented in S2S models. To do this, we look at hindcasts – forecasts initialised for dates in the past – from 10 different prediction systems from around the world.  

We find that while all the S2S models represent the spatial pattern of these two EOFs very well, some have biases in the variance explained by the EOFs, particularly at weeks 3 and 4 (Figure 4). Broadly, all the models have more variance explained by their first EOF compared with ERA5, and less by the second EOF – but this bias is particularly large for the three models with the lowest horizontal resolution (BoM, CMA, and HMCR).  

Figure 4: Weekly-mean ratio between the variance explained by the EOFs in each model and the ERA5 EOF. [Figure 6 in Lee et al. (2020)] 

Additionally, we find that the deterministic prediction skill in the S-G pattern (measured by the ensemble-mean correlation) can be as small as 5-6 days for the BoM model – and only as high as 11 days in the higher resolution models. Extending this to probabilistic skill in weeks 3 and 4, we find models have only limited (if any) skill above climatology in weeks 3 and 4 (and much less than the skill in the leading EOF, the NAO-like pattern).  

Furthermore, we find that the relationship between the S-G pattern and the enhanced heat flux in the stratosphere decays with lead-time in most S2S models, even in the higher-resolution models (Figure 5). Thus, this suggests that the dynamical link between the troposphere and stratosphere weakens with lead time in these models – so even a correct tropospheric prediction may not, in these cases, have a subsequently accurate extended-range stratospheric forecast. 

Figure 5: Weekly mean regression coefficients between the S–G index and the corresponding eddy heat flux anomalies at (a) 300 hPa on the same day, (b) 100 hPa three days later, and (c) 50 hPa four days later. The lags correspond to days with maximum correlation in ERA5. Stippled bars indicate a significant difference from ERA5 at the 95% confidence level. [Figure 11 in Lee et al. (2020)] 

So, when taking this all together, we have: 

  • The S-G pattern is the second-leading mode of MSLP variability in the northeast Atlantic during winter. 
  • It is associated with enhanced vertically propagating wave activity into the stratosphere and a weakened polar vortex in the following weeks to months. 
  • S2S models represent the spatial patterns of the two leading EOFs well. 
  • Most S2S models have a zonal variability bias, with relatively more variance explained by the leading EOF and correspondingly less in the second EOF.  
  • This bias is largest in the lowest-resolution models in weeks 3 and 4.  
  • Extended range skill in the S-G pattern is low, and lower than for the NAO-like zonal pattern. 
  • The linear relationship between the S-G pattern and eddy heat flux in the stratosphere decays with lead-time in most S2S models.  

The zonal variance bias is consistent with S2S model biases in Rossby wave breaking and blocking, while these biases have been widely found to be largest in the lowest resolution models. The results suggest that the poor prediction of the S-G event in February 2018 is not unique to that case, but a more generic issue. Overall, the combination of the variability biases, the poor extended-range predictability, and the poor representation of its impact on the stratospheric vortex at longer lead-times likely contributes to limiting skill at predicting major SSWs on S2S timescales – which remains low, despite the stratosphere’s much longer timescales. Correcting the biases outlined here will likely contribute to improving this skill, and subsequently increasing how far we are able to predict real-world weather.   

How Important are Post-Tropical Cyclones to European Windstorm Risk?

Elliott Sainsbury, e.sainsbury@pgr.reading.ac.uk

To date, the 2020 North Atlantic hurricane season has been the most active on record, producing 20 named storms, 7 hurricanes, and a major hurricane which caused $9 billion in damages across the southern United States. With the potential for such destructive storms, it is understandable that a large amount of attention is paid to the North Atlantic basin at this time of year. Whilst hurricanes have been known to cause devastation in the tropics for centuries, until recently there was little appreciation for the destructive potential of these systems across Europe.

As tropical cyclones such as hurricanes move poleward – away from the tropics and into regions of lower sea surface temperatures and higher vertical wind shear, they undergo a process called extratropical transition (Klein et al., 2000): Over a period of time, the cyclones change from symmetric, warm cored systems into asymmetric cold core systems fuelled by horizontal temperature gradients, as opposed to latent heat fluxes (Evans et al., 2017). These systems, so-called post-tropical cyclones (PTCs), often reintensify in the mid-latitude Atlantic with consequences for land masses downstream – often Europe. This was highlighted in 2017, when ex-hurricane Ophelia impacted Ireland, bringing with it the strongest winds Ireland had seen in 50 years (Stewart, 2018). 3 people were killed, and 360,000 homes were without power.

In a recent paper, we quantify the risk associated with PTCs across Europe relative to mid-latitude cyclones (MLCs) for the first time – in terms of both the absolute risk (i.e. what fraction of high impact wind events across Europe are caused by PTCs?) and also the relative risk (for a given PTC, how likely is it to be associated with high-impact winds, and how does this compare to a given MLC?). By tracking all cyclones impacting a European domain (36-70N, 10W-30E) in the ERA5 reanalysis (1979-2017) using a feature tracking algorithm (Hodges, 1994, 1995, 1999), we identify the post-tropical cyclones using spatiotemporal matching (Hodges et al., 2017) with the observational record, IBTrACS (Knapp et al., 2010).

Figure 1: Distributions of the maximum intensity (maximum wind speed, minimum MSLP) attained by each PTC and MLC inside (a-c) the whole European domain (36-70N, 10W-30E), (d-f) the Northern Europe domain (48-70N, 10W-30E) and (g-i) the Southern Europe domain (36-48N, 10W-30E), using cyclones tracked through the ERA5 reanalysis all year round, 1979-2017. [Figure 2 in Sainsbury et al. 2020].

Figure 1 shows the distributions of maximum intensity for PTCs and MLCs across the entire European domain (top), Northern Europe (48-70°N, 10°W-30°E; middle) and Southern Europe (36-48°N, 10°W-30°E; bottom), using all cyclone tracks all year round. The distribution of PTC maximum intensities is higher (in terms of both wind speed and MSLP) than MLCs, particularly across Northern Europe. The difference between the maximum intensity distributions of PTCs and MLCs across Northern Europe is statistically significant (99%). PTCs are also present in the highest of intensity bins, indicating that the strongest PTCs have intensities comparable to strong wintertime MLCs.

Whilst Figure 1 shows that PTCs are stronger than MLCs even when considering MLCs forming all year round (including the often much stronger wintertime MLCs), it is also useful to compare the risks posed by PTCs relative to MLCs forming at the same time of the year – during the North Atlantic hurricane season (June 1st-November 30th).

Figure 2 shows the fraction of all storms, binned by their maximum intensity in their respective domains, which are PTCs. For storms with weak-moderate maximum winds (first three bins in the figure), <1% of such events are caused by PTCs (with the remaining 99% caused by MLCs). For stronger storms, particularly those of storm force (>25 ms-1 on the Beaufort scale), this percentage is much higher. Despite less than 1% of all storms impacting Northern Europe during hurricane season being PTCs, almost 9% of all storms with storm-force winds which impact the region are PTCs, suggesting that a disproportionate fraction of high-impact windstorms are PTCs. 8.2% of all Northern Europe impacting PTCs which form during hurricane season impact the region with storm-force winds. This fraction is only 0.8% for MLCs, suggesting that the fraction of PTCs impacting Northern Europe with storm-force winds is approximately 10 times greater than MLCs.

Figure 2: The fraction of cyclones impacting Europe which are PTCs as a function of their maximum 10m wind speed in their respective domain. Lower bound of wind speed is shown on the x axis, bin width = 3. Error bars show the 95% confidence interval. All cyclone tracks forming during the North Atlantic hurricane season are used. [Figure 4 in Sainsbury et al. 2020].

Here we have shown that PTCs, at their maximum intensity over Northern Europe, are stronger than MLCs. However, the question still remains as to why this is the case. Warm-seclusion storms post-extratropical transition have been shown to have the fastest rates of reintensification (Kofron et al., 2010) and typically have the lowest pressures upon impacting Europe (Dekker et al., 2018). Given the climatological track that PTCs often take over the warm waters of the Gulf stream, along with the contribution of both baroclinic instability and latent heat release for warm-seclusion development (Baatsen et al., 2015), one hypothesis may be that PTCs are more likely to develop into warm seclusion storms than the broader class of mid-latitude cyclones, potentially explaining the disproportionate impacts they cause across Europe. This will be the topic of future work.

Despite PTCs disproportionately impacting Europe with high intensities, they are a relatively small component of the total cyclone risk in the current climate. However, only small changes are expected in MLC number and intensity under RCP 4.5 (Zappa et al., 2013). Conversely, the number of hurricane-force (>32.6 ms-1) storms impacting Norway, the North Sea and the Gulf of Biscay has been projected to increases by a factor of 6.5, virtually all of which originate in the tropics (Haarsma et al., 2013). Whilst the absolute contribution of PTCs to hurricane season windstorm risk is currently low, PTCs may make an increasingly significant contribution to European windstorm risk in a future climate.

Interested to read more? Read our paper, published in Geophysical Research Letters.

Sainsbury, E. M., R. K. H. Schiemann, K. I. Hodges, L. C. Shaffrey, A. J. Baker, K. T. Bhatia, 2020: How Important Are Post‐Tropical Cyclones for European Windstorm Risk? Geophysical Research Letters, 47(18), e2020GL089853, https://doi.org/10.1029/2020GL089853

References

Baatsen, M., Haarsma, R. J., Van Delden, A. J., & de Vries, H. (2015). Severe Autumn storms in future Western Europe with a warmer Atlantic Ocean. Climate Dynamics, 45, 949–964. https://doi.org/10.1007/s00382-014-2329-8

Dekker, M. M., Haarsma, R. J., Vries, H. de, Baatsen, M., & Delden, A. J. va. (2018). Characteristics and development of European cyclones with tropical origin in reanalysis data. Climate Dynamics, 50(1), 445–455. https://doi.org/10.1007/s00382-017-3619-8

Evans, C., Wood, K. M., Aberson, S. D., Archambault, H. M., Milrad, S. M., Bosart, L. F., et al. (2017). The extratropical transition of tropical cyclones. Part I: Cyclone evolution and direct impacts. Monthly Weather Review, 145(11), 4317–4344. https://doi.org/10.1175/MWR-D-17-0027.1

Haarsma, R. J., Hazeleger, W., Severijns, C., De Vries, H., Sterl, A., Bintanja, R., et al. (2013). More hurricanes to hit western Europe due to global warming. Geophysical Research Letters, 40(9), 1783–1788. https://doi.org/10.1002/grl.50360

Hodges, K., Cobb, A., & Vidale, P. L. (2017). How well are tropical cyclones represented in reanalysis datasets? Journal of Climate, 30(14), 5243–5264. https://doi.org/10.1175/JCLI-D-16-0557.1

Hodges, K. I. (1994). A general method for tracking analysis and its application to meteorological data. Monthly Weather Review, 122(11), 2573–2586. https://doi.org/10.1175/1520-0493(1994)122<2573:AGMFTA>2.0.CO;2

Hodges, K. I. (1995). Feature Tracking on the Unit Sphere. Monthly Weather Review, 123(12), 3458–3465. https://doi.org/10.1175/1520-0493(1995)123<3458:ftotus>2.0.co;2

Hodges, K. I. (1999). Adaptive constraints for feature tracking. Monthly Weather Review, 127(6), 1362–1373. https://doi.org/10.1175/1520-0493(1999)127<1362:acfft>2.0.co;2

Klein, P. M., Harr, P. A., & Elsberry, R. L. (2000). Extratropical transition of western North Pacific tropical cyclones: An overview and conceptual model of the transformation stage. Weather and Forecasting, 15(4), 373–395. https://doi.org/10.1175/1520-0434(2000)015<0373:ETOWNP>2.0.CO;2

Knapp, K. R., Kruk, M. C., Levinson, D. H., Diamond, H. J., & Neumann, C. J. (2010). The international best track archive for climate stewardship (IBTrACS). Bulletin of the American Meteorological Society, 91(3), 363–376. https://doi.org/10.1175/2009BAMS2755.1

Kofron, D. E., Ritchie, E. A., & Tyo, J. S. (2010). Determination of a consistent time for the extratropical transition of tropical cyclones. Part I: Examination of existing methods for finding “ET Time.” Monthly Weather Review, 138(12), 4328–4343. https://doi.org/10.1175/2010MWR3180.1

Stewart, S. R. (2018). Tropical Cyclone Report: Hurricane Ophelia. National Hurricane Center, (February), 1–32. https://doi.org/AL142016

Zappa, G., Shaffrey, L. C., Hodges, K. I., Sansom, P. G., & Stephenson, D. B. (2013). A multimodel assessment of future projections of North Atlantic and European extratropical cyclones in the CMIP5 climate models. Journal of Climate, 26(16), 5846–5862. https://doi.org/10.1175/JCLI-D-12-00573.1

Exploring the impact of variable floe size on the Arctic sea ice

Email: a.w.bateson@pgr.reading.ac.uk

The Arctic sea ice cover is made up of discrete units of sea ice area called floes. The size of these floes has an impact on several sea ice processes including the volume of melt produced at floe edges, the momentum exchange between the sea ice, ocean, and atmosphere, and the mechanical response of the sea ice to stress. Models of the sea ice have traditionally assumed that floes adopt a uniform size, if floe size is explicitly represented at all in the model. Observations of floes show that floe size can span a huge range, from scales of metres to tens of kilometres. Generally, observations of the floe size distribution (FSD) are fitted to a power law or a combination of power laws (Stern et al., 2018a).

The Los Alamos sea ice model, hereafter referred to as CICE, usually assumes a fixed floe size of 300 m. We can impose a simple FSD model into CICE derived from a power law to explore the impact of variable floe size on the sea ice cover. Figure 1 is a diagram of the WIPoFSD model (Waves-in-Ice module and Power law Floe Size Distribution model), which assumes a power law with a fixed exponent, \alpha, between a lower floe size cut-off, d_{min}, and an upper floe size cut-off, d_{max}. The model also incorporates a floe size variable, l_{var}, to capture the effects of processes that can influence floe size. The processes represented are wave break-up of floes, melting at the floe edge, winter floe growth, and advection. The model includes a wave advection and attenuation scheme so that wave properties can be determined within the sea ice field to enable the identification of wave break-up events. Full details of the WIPoFSD model and its implementation into CICE are available in Bateson et al. (2020). For the WIPoFSD model setup considered here, we explore the impact of the FSD on the lateral melt rate, which is the melt rate at the edge surfaces of floes. It is useful to define a new FSD metric that can be used to characterise the impact of the FSD on lateral melt. To do this we note that the lateral melt volume produced by a floe is proportional to the perimeter of the floe. The effective floe size, l_{eff}, is defined as a fixed floe size that would produce the same lateral melt rate as a given FSD, for a fixed total sea ice area.

Figure 1: A schematic of the imposed FSD model. This model is initiated by prescribing a power law with an exponent, \alpha, and between the limits d_{min} and d_{max}. Within individual grid cells the variable FSD tracer, l_{var}, varies between these two limits. l_{var} evolves through lateral melting, wave break-up events, freezing, and advection.

Here we will compare a CICE simulation incorporating the WIPoFSD model, hereafter referred to as stan-fsd, to a reference case, ref, using the CICE standard fixed floe size of 300 m. For the WIPoFSD model, d_{min} = 10 m, d_{max} = 30 km, and \alpha = -2.5. These values have been selected as representative values from observations. The reference setup is initiated in 1990 and spun-up until 2005, when either continued as ref or the WIPoFSD model imposed for stan-fsd before being evaluated from 2006 – 2016. All figures in this post are given as a mean over 2007 – 2016, such that 2005 – 2006 is a period of spin-up for the incorporated WIPoFSD model.

In Figure 2, we show the percentage reduction in the Arctic sea ice extent and volume of stan-fsd relative to ref. The differences in both extent and volume over the pan-Arctic scale evolve over an annual cycle, with maximum differences of -1.0 % in August and -1.1 % in September respectively. The annual cycle corresponds to periods of melting and freeze-up and is a product of the nature of the imposed FSD. Lateral melt rates are a function of floe size, but freeze-up rates are not, hence model differences only increase during periods of melting and not during periods of freeze-up. The difference in sea ice extent reduces rapidly during freeze-up because this freeze-up is predominantly driven by ocean surface properties, which are strongly coupled to atmospheric conditions in areas of low sea ice extent. In comparison, whilst atmospheric conditions initiate the vertical sea ice growth, this atmosphere-ocean coupling is rapidly lost due to insulation of the warmer ocean from the cooler atmosphere once sea ice extends across the horizontal plane. Hence a residual difference in sea ice thickness and therefore volume propagates throughout the winter season. The interannual variability shows that the impact of the WIPoFSD model with standard parameters varies significantly depending on the year.

Figure 2: Difference in sea ice extent (solid, red ribbon) and volume (dashed, blue ribbon) between stan-fsd relative to ref averaged over 2007–2016. The ribbon shows the region spanned by the mean value plus or minus 2 times the standard deviation for each simulation. This gives a measure of the interannual variability over the 10-year period.

Although the pan-Arctic differences in extent and volume shown in Figure 2 are marginal, differences are larger when considering smaller spatial scales. Figure 3 shows the spatial distribution in the changes in sea ice concentration and thickness in March, June, and September for stan-fsd relative to ref in addition to the spatial distribution in l_{eff} for stan-fsd for the same months. Reductions in the sea ice concentration and thickness of up to 0.1 and 50 cm observed respectively in the September marginal ice zone (MIZ). Within the pack ice, increases in the sea ice concentration of up to 0.05 and ice thickness of up to 10 cm can be seen. To understand the non-uniform spatial impacts of the FSD, it is useful to look at the behaviour of l_{eff}. Regions with an l_{eff} greater than 300 m will experience less lateral melt than the equivalent location in ref (all other things being equal) whereas locations with an l_{eff} below 300 m will experience more lateral melt. In Figure 3 we see the transition to values of l_{eff} smaller than 300 m in the MIZ, hence most of the sea ice cover experiences less lateral melting for stan-fsd compared to ref.

Figure 3: Difference in the sea ice concentration (top row, a-c) and thickness (middle row, d-f) between stan-fsd and ref and l_{eff} (bottom row, g-i) for stan-fsd averaged over 2007 – 2016. Results are presented for March (left column, a, d, g), June (middle column, b, e, h) and September (right column, c, f, i). Values are shown only in locations where the sea ice concentration exceeds 5 %.

For Figures 2-3, the parameters used to define the FSD have been set to fixed, standard values. However, these parameters vary significantly between different observed FSDs. It is therefore useful to explore the model sensitivity to these parameters. For α values of -2, -2.5, -3 and -3.5 have been selected to span the general range of values reported in observations (Stern et al., 2018a). For d_{min} values of 1 m, 20 m and 50 m are selected to reflect the different behaviours reported in studies, with some showing power law behaviour extending to 1 m (Toyota et al., 2006) and others showing a tailing off at an order of 10 s of metres (Stern et al., 2018b). For the upper cut-off, d_{max}, values of 1000 m, 10,000 m, 30,000 m and 50,000 m are selected, again to represent the distributions reported in different studies. 50 km is taken as the largest value for d_{max} as this serves as an upper limit to what can be resolved within an individual grid cell on a CICE 1^{\circ} grid. A total of 19 sensitivity studies have been completed used different permutations of the stated values for the FSD model parameters. Figure 4 shows the change in mean September sea ice extent and volume relative to ref plotted against mean annual l_{eff}, averaged over the sea ice extent, for each of these sensitivity studies. The impacts range from a small increase in extent and volume to large reductions of -22 % and -55 % respectively, even within the parameter space defined by observations. Furthermore, there is almost a one-to-one mapping between mean l_{eff} and extent and volume reduction. This suggests l_{eff} is a useful diagnostic tool to predict the impact of a given set of floe size parameters. The system varies most in response to the changes in the α, but it is also particularly sensitive to d_{min}.

Figure 4: Relative change (%) in mean September sea ice volume from 2007 – 2016 respectively, plotted against mean l_{eff} for simulations with different selections of parameters relative to ref. The mean l_{eff} is taken as the equally weighted average across all grid cells where the sea ice concentration exceeds 15%. The colour of the marker indicates the value of the \alpha, the shape indicates the value of d_{min}, and the three experiments using standard parameters but different d_{max} (1000 m, 10000 m and 50000 m) are indicated by a crossed red square. The parameters are selected to be representative of a parameter space for the WIPoFSD model that has been constrained by observations.

There are several advantages to the assumption of a fixed power law in modelling the sea ice floe size distribution. It provides a simple framework to explore the potential impact of an observed FSD on the sea ice mass balance, given observations of the FSD are generally fitted to a power law. In addition, the use of a simple model makes it easier to constrain the mechanism of how the model changes the sea ice cover. However, there are also significant disadvantages including the high model sensitivity to poorly constrained parameters, as shown in Figure 4. In addition, there is evidence both that the exponent evolves over an annual cycle and is not a fixed value (Stern et al., 2018b) and that the power law is not a statistically valid description of the FSD over all floe sizes (Horvat et al., 2019). An alternative approach to modelling the FSD is the prognostic model of Roach et al. (2018, 2019). The prognostic model avoids any assumptions about the shape of the distribution and instead assigns sea ice area to a set of adjacent floe size categories, with individual processes parameterised at floe scale. This approach carries its own set of challenges. If important physical processes are missing from the model it will not be possible to simulate a physically realistic distribution. In addition, the prognostic model has a significant computational cost. In practice, the choice of FSD modelling approach will depend on the application.

Further reading
Bateson, A. W., Feltham, D. L., Schröder, D., Hosekova, L., Ridley, J. K. and Aksenov, Y.: Impact of sea ice floe size distribution on seasonal fragmentation and melt of Arctic sea ice, Cryosphere, 14, 403–428, https://doi.org/10.5194/tc-14-403-2020, 2020.

Horvat, C., Roach, L. A., Tilling, R., Bitz, C. M., Fox-Kemper, B., Guider, C., Hill, K., Ridout, A., and Shepherd, A.: Estimating the sea ice floe size distribution using satellite altimetry: theory, climatology, and model comparison, The Cryosphere, 13, 2869–2885, https://doi.org/10.5194/tc-13-2869-2019, 2019. 

Stern, H. L., Schweiger, A. J., Zhang, J., and Steele, M.: On reconciling disparate studies of the sea-ice floe size distribution, Elem. Sci. Anth., 6, p. 49, https://doi.org/10.1525/elementa.304, 2018a. 

Stern, H. L., Schweiger, A. J., Stark, M., Zhang, J., Steele, M., and Hwang, B.: Seasonal evolution of the sea-ice floe size distribution in the Beaufort and Chukchi seas, Elem. Sci. Anth., 6, p. 48, https://doi.org/10.1525/elementa.305, 2018b. 

Roach, L. A., Horvat, C., Dean, S. M., and Bitz, C. M.: An Emergent Sea Ice Floe Size Distribution in a Global Coupled Ocean-Sea Ice Model, J. Geophys. Res.-Oceans, 123, 4322–4337, https://doi.org/10.1029/2017JC013692, 2018. 

Roach, L. A., Bitz, C. M., Horvat, C. and Dean, S. M.: Advances in Modeling Interactions Between Sea Ice and Ocean Surface Waves, J. Adv. Model. Earth Syst., 11, 4167–4181, https://doi.org/10.1029/2019MS001836, 2019.

Toyota, T., Takatsuji, S., and Nakayama, M.: Characteristics of sea ice floe size distribution in the seasonal ice zone, Geophys. Res. Lett., 33, 2–5, https://doi.org/10.1029/2005GL024556, 2006. 

How do ocean and atmospheric heat transports affect sea-ice extent?

Email: j.r.aylmer@pgr.reading.ac.uk

Downward trends in Arctic sea-ice extent in recent decades are a striking signal of our warming planet. Loss of sea ice has major implications for future climate because it strongly influences the Earth’s energy budget and plays a dynamic role in the atmosphere and ocean circulation.

Comprehensive numerical models are used to make long-term projections of the future climate state under different greenhouse gas emission scenarios. They estimate that the Arctic ocean will become seasonally ice free by the end of the 21st century, but there is a large uncertainty on the timing due to the spread of estimates across models (Fig. 1).

Figure 1: Projections of Arctic sea-ice extent under ‘moderate’ emissions in 20 recent-generation climate models. Model data: CMIP6 multi-model ensemble; observational data: National Snow & Ice Data Center.

What causes this spread, and how might it be reduced to better constrain future projections? There are various factors (Notz et al. 2016), but of interest to our work is the large-scale forcing of the atmosphere and ocean. The mean atmospheric circulation transports about 3 PW of heat from lower latitudes into the Arctic, and the oceans transport about a tenth of that (e.g. Trenberth and Fasullo, 2017; 1 PW = 1015 W). Our goal is to understand the relative roles of Ocean and Atmospheric Heat Transports (OHT, AHT) on long timescales. Specifically, how sensitive is the sea-ice cover to deviations in OHT and AHT, and what underlying mechanisms determine the sensitivities?

We developed a highly simplified Energy-Balance Model (EBM) of the climate system (Fig. 2)—it has only latitudinal variations and is described by a few simple equations relating energy transfer between the atmosphere, ocean, and sea ice (Aylmer et al. 2020). The latitude of the sea-ice edge is an analogue for ice extent in the real world. The simplicity of the EBM allows us to isolate the basic physics of the problem, which would not be possible going directly with the complex output of a full climate model.

Figure 2: Simplified schematic of our Energy-Balance Model (EBM; see Aylmer et al. 2020 for technical details). Arrows represent energy fluxes, each varying with latitude, between the atmosphere, ocean, and sea ice.

We generated a set of simulations in which OHT varies and checked the response of the ice edge. This is a measure of the effective sensitivity of the ice cover to OHT (Fig. 3a)—it is not the actual sensitivity because AHT decreases (Fig. 3b), and we are really seeing in Fig. 3a the net response of the ice edge to changes in both OHT and AHT.

Figure 3: (a) Effective sensitivity of the (annual-mean) sea-ice edge to varying OHT (expressed as the mean convergence over the ice pack). (b) AHT convergence reduces at the same time, which partially cancels the true impact of increasing OHT on sea ice.

This reduction in AHT with increasing OHT is called Bjerknes compensation, and it occurs in full climate models too (Outten et al. 2018). Here, it has a moderating effect on the true impact of increasing OHT. With further analysis, we determined the actual sensitivity to be about 1.5 times the effective sensitivity. The actual sensitivity of the ice edge to AHT turns out to be about half that to the OHT.

What sets the difference in OHT and AHT sensitivities? This is easily answered within the EBM framework. We derived a general expression for the ratio of (actual) ice-edge sensitivities to OHT (so) and AHT (sa):

A higher-order term has been neglected for simplicity here, but the basic point remains: the ratio of sensitivities mainly depends on the parameters BOLR and Bdown. These are bulk representations of atmospheric feedbacks and determine the efficiency of outgoing and downwelling longwave radiation, respectively. They are always positive, so the ice edge is always more sensitive to OHT than AHT.

The interpretation of this equation is simple. AHT converging over the ice pack can either be transferred to the underlying sea ice, or radiated to space, having no impact on the ice, and the partitioning is controlled by Bdown and BOLR. The same amount of OHT converging under the ice pack can only go through the ice and is thus the more efficient driver.

Climate models with larger OHTs tend to have less sea ice (Mahlstein and Knutti, 2011). We have also found strong correlations between OHT and the sea-ice edge in several of the models listed in Fig. 1 individually. Ice-edge sensitivities and B values can be determined per model, and our equation predicts how these should be related. Our work thus provides a way to investigate how much physical biases in OHT and AHT contribute to sea-ice-projection uncertainties.

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.

Figure 1: (a) Arctic September sea ice extent from 1979-2019. (b) Spatial distribution of Arctic September sea ice extent in 1980. (c) Spatial distribution of Arctic September sea ice extent in 2019. Images have been obtained from NSIDC (2020).

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.

Figure 2: Climatological track density of all Arctic storms that travel north of 65°N between 1980/81–2016/17 in (a) winter (DJF) and 1980–2017 in (b) summer (JJA) based on the ERA-Interim reanalysis. Densities have units of number per season per unit area (5° spherical cap, ≈ 10^{6} km^{2}). Longitudes are shown every 60°E, and latitudes are shown at 80°N, 65°N (bold) and 50°N. Figure from Vessey at al. (2020).

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.

Read more at: https://link.springer.com/article/10.1007/s00382-020-05142-4

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.

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.

Figure 1: Growth of error energy spectra (red, bottom to top) in the Lorenz (1969) model under the influence of a control spectrum (blue) of slope (left) -3 and (right) -\frac{5}{3}.

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.

Figure 2: As in Figure 1, except that the control spectrum is a hybrid spectrum with a -3 range in the synoptic scale and a -\frac{5}{3} range in the mesoscale, truncating at (left) K_{max}=11 and (right) K_{max}=21. The colours red and blue are reversed compared to Figure 1.

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.

Figure 3: The parameter a as a function of the scale K, for truncations (left) K_{max}=8,9,10,11 and (right) K_{max}=11,13,15,17,19,21.

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

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.
Figure 1: Probability density function of eddy lifetime (left) and zonal average of eddy lifetime (right). Both plots use eddies with lifetimes longer than 1 month.
  • 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.
Figure 2: Eddy genesis (number of eddies per year) for eddies lasting longer than 1 week (binned to 1 degree x 1 degree boxes).
  • 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.
Figure 3: Probability density functions (pdf) of the lifetime-averaged eddy radius (Lspd): a normalized pdf on a linear scale with 2km bins. The black dotted lines are plotted on the medians for each resolution: the median values are 48km, 32km and 14km for observations, EP and ER resolution respectively. (The blue dotted lines can be ignored, see Moreton et al. [2020]).

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

s.h.lee@pgr.reading.ac.uk

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.

Figure 1: 500 hPa geopotential height anomalies for the four North American weather regimes. Anomalies are expressed with respect to a linearly de-trended 1979-2017 base period. Stippling indicates significance at the 95% confidence level according to a two-sided bootstrap re-sampling test.

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.

Figure 2: Probabilities of (a) occurrence, (b) persistence, and (c) transition from another regime into each regime stratified by the tercile anomaly categories of 100 hPa 60°N zonal-mean zonal wind. Error bars indicate 95% binomial proportion confidence intervals where the sample size has been scaled to account for lag-1 autocorrelation.

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).

Figure 3: Proportion of days assigned into each regime over the period 1 January 1979-31 December 2017 (DJFM days only) where normalised temperatures dropped below -1.5 standard deviations. Stippling indicates 95% confidence according to a one-sided bootstrap re-sampling test.

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.

Sudden Stratospheric Warming does not always equal Sudden Snow Shoveling

Email: s.h.lee@pgr.reading.ac.uk

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).

Figure 1: The Arctic stratospheric polar vortex, here shown at 10 hPa, on March 12, 2019. Geopotential height is contoured, and filled colours show the wind speed in m/s. The zonal-mean zonal wind at 60°N is shown in the bottom left, a commonly used diagnostic of the strength of the SPV. After Figure 6 in Lee and Butler (2019).

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.

Figure 2: As in Figure 1 but for 2 January 2019 (after Figure 4 in Lee and Butler (2019)).

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!

Figure 3: Average surface temperature anomaly for days 0-30 following all major SSWs in ERA-Interim 1979-2014. [Source: SSW Compendium]

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.

Figure 4: 60-90°N geopotential height anomaly time-height cross-section for August 2018-May 2019. Vertical dashed lines indicate (left-right) the SPV spin-up, the major SSW, a strong vortex event (Tripathi et al. 2015), and the vortex dissipation. (After Figure 8 in Lee and Butler (2019).)

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 Variation of Geomagnetic Storm Duration with Intensity

Email: carl.haines@pgr.reading.ac.uk


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).

Figure 1: The mean duration (red) and number of storms (blue) plotted as a function of storm intensity.

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.

Figure 2: The distribution of duration for storms with a peak between 150 and 190nT.

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.

Figure 3: (Left) The mean of the log-space as a function of intensity. (Right) The standard deviation of the log-space as a function of intensity.

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.

For more information, please see the open-access paper.

Figure 4: The probability that a storm will last at least 24 hours plotted as a function of storm intensity. The black line shows the observed probability and the red line shows the model output.