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

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

Forecasting lightning is a difficult problem due to the complexity of the lightning process and how dependent the lightning forecast is on the accuracy of the convective forecast. In order to verify forecasts of lightning independently of the accuracy of the convective forecast, it can be helpful to introduce a lightning scheme that is more complex and physically representative than the simple lightning parameterisations often used in Numerical Weather Prediction (NWP).

The existing method of predicting lightning in the Met Office’s Unified Model (MetUM) uses upwards graupel flux and total ice water path, based on the method of McCaul et al. (2009). However, this method tends to overpredict the total number and coverage of lighting, particularly in the UK.

I’ve implemented a physically based, explicit electrification scheme in the MetUM in order to try and improve the current lightning forecasts. The processes involved in the scheme are shown in the flowchart in Figure 1. The electrification scheme uses the Non-Inductive Charging (NIC) process to separate charge within thunderstorms (Mansell et al., 2005; Saunders and Peck, 1998). The NIC theory states that when graupel and ice crystals collide some charge is transferred from one particle to the other. The sign and the magnitude of the charge that is transferred to the graupel particle depends on a number of parameters. It is affected by the ice crystal diameter, the velocity of the collision, the liquid water content and the temperature at which the collision occurs. Once the charge has been generated on graupel and ice or snow particles, it can be moved around the model domain and can be transferred between hydrometeor species. Charge is removed from hydrometeor species and the domain when the hydrometeors precipitate to the surface or if the hydrometeor evaporates or sublimates. Charge is transferred between hydrometeor species proportionally to the mass that is transferred. Charge is held on graupel, rain and cloud ice (or aggregates and crystals if these are included separately).

Figure 1: A flowchart showing the process and order of those processes involved within the new electrification scheme.

Once these charged hydrometeors are distributed through the cloud, they can be totalled to create a charge density distribution. From this distribution the electric field can be calculated. Then from the electric field lightning flashes can be discharged. Lightning flashes are discharged based on two thresholds, the first of these is the initiation threshold and governs where the initiation point for the lightning channel should be (Marshall et al., 1995). The second of these is a propagation threshold and governs whether or not the lightning channel can move through a grid box (Barthe et al., 2012). Lightning channels are only allowed to propagate vertically within a grid column to simplify the model structure (Fierro et al., 2013). Once the channel is created charge is neutralised along the channel, charge is removed from hydrometeor species in both the channel and the grid points immediately adjacent to the channel.

The updated charge density distribution is then used to recalculate the electric field and new flashes are discharged from any points that exceed the electric field threshold. This process keeps repeating until no new lightning flashes are discharged within the domain.

The plots in Figure 2 show the charge on graupel (a), cloud ice (b), rain (c) and the total charge (d) for a small single cell thunderstorm in the south of the UK on the 31st August 2017. It can be seen in these figure that the charge is mainly positive on cloud ice and mainly negative on graupel. The cloud ice, being less dense is lofted towards the top of the thunderstorm, while the graupel being denser generally falls towards the bottom of the storm. This creates the charge structure seen in Fig. 2d, with two positive-negative dipoles. This charge structure allows for the development of strong electric fields between the positive and negative charge centres in each dipole. If the electric field between the charge centres reaches the order of 100s kVm-1 the air can become electrically conductive, causing lightning.

Figure 2: The charge on hydrometeors in a small single-cell thunderstorm (a) shows the charge on graupel, (b) shows the charge on cloud ice, (c) shows the charge on rain and (d) shows total charge. In each plot, the outline indicated by the solid black line is the 5 dBZ reflectivity contour.

The electrification scheme was run within the operational configuration of the MetUM for a case study. The case study was a case of some organised and some single-cell, fair weather convection, on the 31st August 2017. The observations of lightning flashes are taken from the Met Office’s ATDNet lightning location system. The results of the total lighting accumulated for the entire day of the 31st August are shown in Figure 3. It can be easily seen that the existing method is producing far too much lightning compared to the observations. The new scheme is much closer to the observations.

It is an improvement, not only in the total lightning output, but also in the appearance of the lightning flash map. The scattered nature of the observations is captured by the new scheme, whereas the existing parameterisation appears to be largely producing lightning in neat, contoured paths. These paths show that the way that the existing parameterisation predicts lightning is not physically accurate and indicate the problem with the parameterisation, namely that it relies too heavily on the total ice water path. The new scheme suggests a possible improvement, in considering more explicitly the combination of graupel, liquid water and cloud ice that is vital for the production of charge and therefore lightning.

Figure 3: The total lightning flash accumulation for 31st August 2017 across the UK, (a) shows the output of the new electrification scheme, (b) shows the observed flashes, binned to match the model grid, and (c) shows the output of the existing MetUM parameterisation.

References:
Barthe, C., Chong, M., Pinty, J.-P., and Escobar, J. (2012). CELLS v1.0: updated and parallelized version of an electrical scheme to simulate multiple electrified clouds and flashes over large domains. Geoscientific Model Development, (5), 167–184.

Fierro, A. O., Mansell, E. R., MacGorman, D. R., and Ziegler, C. L. (2013). The Implementation of an Explicit Charging and Discharge Lightning Scheme within the WRF-ARW Model: Benchmark Simulations of a Continental Squall Line, a Tropical Cyclone, and a Winter Storm. Monthly Weather Review, 141, 2390–2415.

Mansell, E. R., MacGorman, D. R., Ziegler, C. L., and Straka, J. M. (2005). Charge structure and lightning sensitivity in a simulated multicell thunderstorm. Journal of Geophysical Research, 110.

Marshall, T. C., McCarthy, M. P., and Rust, W. D. (1995). Electric field magnitudes and lightning initiation in thunderstorms. Journal of Geophysical Research, 100, 7097–7103.

McCaul, E. W., Goodman, S. J., LaCasse, K. M., and Cecil, D. J. (2009). Forecasting lightning threat using cloud-resolving model simulations. Weather and Forecasting, 24(3), 709–729.

Saunders, C. P. R. and Peck, S. L. (1998). Laboratory studies of the influence of the rime accretion rate on charge transfer during crystal / graupel collisions. Journal of Geophysical Research, 103, 949–13.

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

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

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

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.

Life on Industrial Placement

Email: holly.turner@reading.ac.uk

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

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

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

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

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

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

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

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

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

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.

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.