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.

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

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 impact of atmospheric model resolution on the Arctic

Email: sally.woodhouse@pgr.reading.ac.uk

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.

Stroeve_et_al-2012-fig2a
Figure 1. Time-series of September sea ice extent from 20 CMIP5 models (colored lines), individual ensemble members are dotted lines and the individual model mean is solid. Multi-model ensemble mean from a subset of the models is shown in solid black with +/- 1 standard deviation in dotted black. The red line shows observations. From Stroeve et al. (2012)

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).

sea_ice_concentration_obs_GC2
Figure 2. Annual mean sea ice concentration for observations (HadISST) and the bias of each different experiment from the observations N96: low resolution, N216: medium resolution, N512: high resolution.

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.)

strait_locations
Location of ocean gateways into the Arctic. Red: Bering Strait, Green: Davis Strait, Blue: Fram Strait, Magenta: Barents Sea

ocean_heat_transport_GC2
Figure 3. Ocean energy transport for each resolution experiment through the four ocean gateways into the Arctic. The four gateways form a closed boundary into the Arctic.

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

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.

How much energy is available in a moist atmosphere?

Email: b.l.harris@pgr.reading.ac.uk

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.

Figure 1: Construction of the APE reference state for a 2D atmosphere. The purple shading indicates the density of the air; darker colours mean denser air. In the actual state, the density stratification is not completely horizontal, which leads to the air motion shown by the orange arrows. The reference state has a stable, horizontal density stratification, so the air will not move without some disturbance.

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