Modelling windstorm losses in a climate model

Extratropical cyclones cause vast amounts of damage across Europe throughout the winter seasons. The damage from these cyclones mainly comes from the associated severe winds. The most intense cyclones have gusts of over 200 kilometres per hour, resulting in substantial damage to property and forestry, for example, the Great Storm of 1987 uprooted approximately 15 million trees in one night. The average loss from these storms is over $2 billion per year (Schwierz et al. 2010) and is second only to Atlantic Hurricanes globally in terms of insured losses from natural hazards. However, the most severe cyclones such as Lothar (26/12/1999) and Kyrill (18/1/2007) can cause losses in excess of $10 billion (Munich Re, 2016). One property of extratropical cyclones is that they have a tendency to cluster (to arrive in groups – see example in Figure 1), and in such cases these impacts can be greatly increased. For example Windstorm Lothar was followed just one day later by Windstorm Martin and the two storms combined caused losses of over $15 billion. The large-scale atmospheric dynamics associated with clustering events have been discussed in a previous blog post and also in the scientific literature (Pinto et al., 2014; Priestley et al. 2017).

Picture1
Figure 1. Composite visible satellite image from 11 February 2014 of 4 extratropical cyclones over the North Atlantic (circled) (NASA).

A large part of my PhD has involved investigating exactly how important the clustering of cyclones is on losses across Europe during the winter. In order to do this, I have used 918 years of high resolution coupled climate model data from HiGEM (Shaffrey et al., 2017) which provides a huge amount of winter seasons and cyclone events for analysis.

In order to understand how clustering affects losses, I first of all need to know how much loss/damage is associated with each individual cyclone. This is done using a measure called the Storm Severity Index (SSI – Leckebusch et al., 2008), which is a proxy for losses that is based on the 10-metre wind field of the cyclone events. The SSI is a good proxy for windstorm loss. Firstly, it scales the wind speed in any particular location by the 98th percentile of the wind speed climatology in that location. This scaling ensures that only the most severe winds at any one point are considered, as different locations have different perspectives on what would be classed as ‘damaging’. This exceedance above the 98th percentile is then raised to the power of 3 due to damage from wind being a highly non-linear function. Finally, we apply a population density weighting to our calculations. This weighting is required because a hypothetical gust of 40 m/s across London will cause considerably more damage than the same gust across far northern Scandinavia, and the population density is a good approximation for the density of insured property. An example of the SSI that has been calculated for Windstorm Lothar is shown in Figure 2.

 

figure_2_blog_2018_new
Figure 2. (a) Wind footprint of Windstorm Lothar (25-27/12/1999) – 10 metre wind speed in coloured contours (m/s). Black line is the track of Lothar with points every 6 hours (black dots). (b) The SSI field of Windstorm Lothar. All data from ERA-Interim.

 

From Figure 2b you can see how most of the damage from Windstorm Lothar was concentrated across central/northern France and also across southern Germany. This is because the winds here were most extreme relative to what is the climatology. Even though the winds are highest across the North Atlantic Ocean, the lack of insured property, and a much high climatological winter mean wind speed, means that we do not observe losses/damage from Windstorm Lothar in these locations.

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Figure 3. The average SSI for 918 years of HiGEM data.

 

I can apply the SSI to all of the individual cyclone events in HiGEM and therefore can construct a climatology of where windstorm losses occur. Figure 3 shows the average loss across all 918 years of HiGEM. You can see that the losses are concentrated in a band from southern UK towards Poland in an easterly direction. This mainly covers the countries of Great Britain, Belgium, The Netherlands, France, Germany, and Denmark.

This blog post introduces my methodology of calculating and investigating the losses associated with the winter season extratropical cyclones. Work in Priestley et al. (2018) uses this methodology to investigate the role of clustering on winter windstorm losses.

This work has been funded by the SCENARIO NERC DTP and also co-sponsored by Aon Benfield.

 

Email: m.d.k.priestley@pgr.reading.ac.uk

 

References

Leckebusch, G. C., Renggli, D., and Ulbrich, U. 2008. Development and application of an objective storm severity measure for the Northeast Atlantic region. Meteorologische Zeitschrift. https://doi.org/10.1127/0941-2948/2008/0323.

Munich Re. 2016. Loss events in Europe 1980 – 2015. 10 costliest winter storms ordered by overall losses. https://www.munichre.com/touch/naturalhazards/en/natcatservice/significant-natural-catastrophes/index.html

Pinto, J. G., Gómara, I., Masato, G., Dacre, H. F., Woollings, T., and Caballero, R. 2014. Large-scale dynamics associated with clustering of extratropical cyclones affecting Western Europe. Journal of Geophysical Research: Atmospheres. https://doi.org/10.1002/2014JD022305.

Priestley, M. D. K., Dacre, H. F., Shaffrey, L. C., Hodges, K. I., and Pinto, J. G. 2018. The role of European windstorm clustering for extreme seasonal losses as determined from a high resolution climate model, Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2018-165, in review.

Priestley, M. D. K., Pinto, J. G., Dacre, H. F., and Shaffrey, L. C. 2017. Rossby wave breaking, the upper level jet, and serial clustering of extratropical cyclones in western Europe. Geophysical Research Letters. https://doi.org/10.1002/2016GL071277.

Schwierz, C., Köllner-Heck, P., Zenklusen Mutter, E. et al. 2010. Modelling European winter wind storm losses in current and future climate. Climatic Change. https://doi.org/10.1007/s10584-009-9712-1.

Shaffrey, L. C., Hodson, D., Robson, J., Stevens, D., Hawkins, E., Polo, I., Stevens, I., Sutton, R. T., Lister, G., Iwi, A., et al. 2017. Decadal predictions with the HiGEM high resolution global coupled climate model: description and basic evaluation, Climate Dynamics, https://doi.org/10.1007/s00382-016-3075-x.

Baroclinic and Barotropic Annular Modes of Variability

Email: l.boljka@pgr.reading.ac.uk

Modes of variability are climatological features that have global effects on regional climate and weather. They are identified through spatial structures and the timeseries associated with them (so-called EOF/PC analysis, which finds the largest variability of a given atmospheric field). Examples of modes of variability include El Niño Southern Oscillation, Madden-Julian Oscillation, North Atlantic Oscillation, Annular modes, etc. The latter are named after the “annulus” (a region bounded by two concentric circles) as they occur in the Earth’s midlatitudes (a band of atmosphere bounded by the polar and tropical regions, Fig. 1), and are the most important modes of midlatitude variability, generally representing 20-30% of the variability in a field.

Southern_Hemi_Antarctica
Figure 1: Southern Hemisphere midlatitudes (red concentric circles) as annulus, region where annular modes have the largest impacts. Source.

We know two types of annular modes: baroclinic (based on eddy kinetic energy, a proxy for eddy activity and an indicator of storm-track intensity) and barotropic (based on zonal mean zonal wind, representing the north-south shifts of the jet stream) (Fig. 2). The latter are usually referred to as Southern (SAM or Antarctic Oscillation) or Northern (NAM or Arctic Oscillation) Annular Mode (depending on the hemisphere), have generally quasi-barotropic (uniform) vertical structure, and impact the temperature variations, sea-ice distribution, and storm paths in both hemispheres with timescales of about 10 days. The former are referred to as BAM (baroclinic annular mode) and exhibit strong vertical structure associated with strong vertical wind shear (baroclinicity), and their impacts are yet to be determined (e.g. Thompson and Barnes 2014, Marshall et al. 2017). These two modes of variability are linked to the key processes of the midlatitude tropospheric dynamics that are involved in the growth (baroclinic processes) and decay (barotropic processes) of midlatitude storms. The growth stage of the midlatitude storms is conventionally associated with increase in eddy kinetic energy (EKE) and the decay stage with decrease in EKE.

ThompsonWoodworth_Fig2a_SAM_2f_BAM(1)
Figure 2: Barotropic annular mode (right), based on zonal wind (contours), associated with eddy momentum flux (shading); Baroclinic annular mode (left), based on eddy kinetic energy (contours), associated with eddy heat flux (shading). Source: Thompson and Woodworth (2014).

However, recent observational studies (e.g. Thompson and Woodworth 2014) have suggested decoupling of baroclinic and barotropic components of atmospheric variability in the Southern Hemisphere (i.e. no correlation between the BAM and SAM) and a simpler formulation of the EKE budget that only depends on eddy heat fluxes and BAM (Thompson et al. 2017). Using cross-spectrum analysis, we empirically test the validity of the suggested relationship between EKE and heat flux at different timescales (Boljka et al. 2018). Two different relationships are identified in Fig. 3: 1) a regime where EKE and eddy heat flux relationship holds well (periods longer than 10 days; intermediate timescale); and 2) a regime where this relationship breaks down (periods shorter than 10 days; synoptic timescale). For the relationship to hold (by construction), the imaginary part of the cross-spectrum must follow the angular frequency line and the real part must be constant. This is only true at the intermediate timescales. Hence, the suggested decoupling of baroclinic and barotropic components found in Thompson and Woodworth (2014) only works at intermediate timescales. This is consistent with our theoretical model (Boljka and Shepherd 2018), which predicts decoupling under synoptic temporal and spatial averaging. At synoptic timescales, processes such as barotropic momentum fluxes (closely related to the latitudinal shifts in the jet stream) contribute to the variability in EKE. This is consistent with the dynamics of storms that occur on timescales shorter than 10 days (e.g. Simmons and Hoskins 1978). This is further discussed in Boljka et al. (2018).

EKE_hflux_cross_spectrum_blog
Figure 3: Imaginary (black solid line) and Real (grey solid line) parts of cross-spectrum between EKE and eddy heat flux. Black dashed line shows the angular frequency (if the tested relationship holds, the imaginary part of cross-spectrum follows this line), the red line distinguishes between the two frequency regimes discussed in text. Source: Boljka et al. (2018).

References

Boljka, L., and T. G. Shepherd, 2018: A multiscale asymptotic theory of extratropical wave, mean-flow interaction. J. Atmos. Sci., in press.

Boljka, L., T. G. Shepherd, and M. Blackburn, 2018: On the coupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., in review.

Marshall, G. J., D. W. J. Thompson, and M. R. van den Broeke, 2017: The signature of Southern Hemisphere atmospheric circulation patterns in Antarctic precipitation. Geophys. Res. Lett., 44, 11,580–11,589.

Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414–432.

Thompson, D. W. J., and E. A. Barnes, 2014: Periodic variability in the large-scale Southern Hemisphere atmospheric circulation. Science, 343, 641–645.

Thompson, D. W. J., B. R. Crow, and E. A. Barnes, 2017: Intraseasonal periodicity in the Southern Hemisphere circulation on regional spatial scales. J. Atmos. Sci., 74, 865–877.

Thompson, D. W. J., and J. D. Woodworth, 2014: Barotropic and baroclinic annular variability in the Southern Hemisphere. J. Atmos. Sci., 71, 1480–1493.

How does plasma from the solar wind enter Earth’s magnetosphere?

Earth’s radiation belts are a hazardous environment for the satellites underpinning our everyday life. The behaviour of these high-energy particles, trapped by Earth’s magnetic field, is partly determined by the existence of plasma waves. These waves provide the mechanisms by which energy and momentum are transferred and particle populations physically moved around, and it’s some of these waves that I study in my PhD.

However, I’ve noticed that whenever I talk about my work, I rarely talk about where this plasma comes from. In schools it’s often taught that space is a vacuum, and while it is closer to a vacuum than anything we can make on Earth, there are enough particles to make it a dangerous environment. A significant amount of particles do escape from Earth’s ionosphere into the magnetosphere but in this post I’ll focus on material entering from the solar wind. This constant outflow of hot particles from the Sun is a plasma, a fluid where enough of the particles are ionised that the behaviour of the fluid is then dominated by electric and magnetic fields. Since the charged particles in a plasma interact with each other, with external electric and magnetic fields, and also generate more fields by moving and interacting, this makes for some weird and wonderful behaviour.

magnetosphere_diagram
Figure 1: The area of space dominated by Earth’s magnetic field (the magnetosphere) is shaped by the constant flow of the solar wind (a plasma predominantly composed of protons, electrons and alpha particles). Plasma inside the magnetosphere collects in specific areas; the radiation belts are particularly of interest as particles there pose a danger to satellites. Credit: NASA/Goddard/Aaron Kaas

When explaining my work to family or friends, I often describe Earth’s magnetic field as a shield to the solar wind. Because the solar wind is well ionised, it is highly conductive, and this means that approximately, the magnetic field is “frozen in” to the plasma. If the magnetic field changes, the plasma follows this change. Similarly, if the plasma flows somewhere, the magnetic field is dragged along with it. (This is known as Alfvén’s frozen in theorem – the amount of plasma in a volume parallel to the magnetic field line remains constant). And this is why the magnetosphere acts as shield to all this energy streaming out of the Sun – while the magnetic field embedded in the solar wind is topologically distinct from the magnetic field of the Earth, there is no plasma transfer across magnetic field lines, and it streams past our planet (although this dynamic pressure still compresses the plasma of the magnetosphere, giving it that typical asymmetric shape in Figure 1).

Of course, the question still remains of how the solar wind plasma enters the Earth’s magnetic field if such a shielding effect exists. You may have noticed in Figure 1 that there are gaps in the shield that the Earth’s dipole magnetic field presents to the solar wind; these are called the cusps, and at these locations the magnetic field connects to the solar wind. Here, plasma can travel along magnetic field lines and impact us on Earth.

But there’s also a more interesting phenomenon occurring – on a small enough scale (i.e. the very thin boundaries between two magnetic domains) the assumptions behind the frozen-in theorem break down, and then we start to see one of the processes that make the magnetosphere such a complex, fascinating and dynamic system to study. Say we have two regions of plasma with opposing orientation of the magnetic field. Then in a middle area these opposing field lines will suddenly snap to a new configuration, allowing them to peel off and away from this tightly packed central region. Figure 2 illustrates this process – you can see that after pushing red and blue field lines together, they suddenly jump to a new configuration. As well as changing the topology of the magnetic field, the plasma at the centre is energised and accelerated, shooting off along the magnetic field lines. Of course even this is a simplification; the whole process is somewhat more messy in reality and I for one don’t really understand how the field can suddenly “snap” to a new configuration.

reconnection
Figure 2: Magnetic reconnection. Two magnetic domains of opposing orientation can undergo a process where the field line configuration suddenly resets. Instead of two distinct magnetic domains, some field lines are suddenly connected to both, and shoot outwards and away, as does the energised plasma.

In the Earth’s magnetosphere there are two main regions where this process is important (Figure 3). Firstly, at the nose of the magnetosphere. The dynamic pressure of the solar wind is compressing the solar wind plasma against the magnetospheric plasma, and when the interplanetary magnetic field is orientated downwards (i.e. opposite to the Earth’s dipole – about half the time) this reconnection can happen. At this point field lines that were solely connected to the Earth or in the solar wind are now connected to both, and plasma can flow along them.

magnetosphere_reconnection_sites
Figure 3: There are two main areas where reconnection happens in Earth’s magnetosphere. Opposing field lines can reconnect, allowing a continual dynamic cycle (the Dungey cycle) of field lines around the magnetosphere. Plasma can travel along these magnetic field lines freely. Credits: NASA/MMS (image) and NASA/Goddard Space Flight Center- Conceptual Image Lab (video)

Then, as the solar wind continues to rush outwards from the Sun, it drags these field lines along with it, past the Earth and into the tail of the magnetosphere. Eventually the build-up of these field lines reaches a critical point in the tail, and boom! Reconnection happens once more. You get a blast of energised plasma shooting along the magnetic field (this gives us the aurora) and the topology has rearranged to separate the magnetic fields of the Earth and solar wind; once more, they are distinct. These dipole field lines move around to the front of the Earth again, to begin this dramatic cycle once more.

Working out when and how these kind of processes take place is still an active area of research, let alone understanding exactly what we expect this new plasma to do when it arrives. If it doesn’t give us a beautiful show of the aurora, will it bounce around the radiation belts, trapped in the stronger magnetic fields near the Earth? Or if it’s not so high energy as that, will it settle in the cooler plasmasphere, to rotate with the Earth and be shaped as the magnetic field is distorted by solar wind variations? Right now I look out my window at a peaceful sunny day and find it incredible that such complicated and dynamic processes are continually happening so (relatively) nearby. It certainly makes space physics an interesting area of research.

Trouble in paradise: Climate change, extreme weather and wildlife conservation on a tropical island.

Joseph Taylor, NERC SCEARNIO DTP student. Zoological Society of London.

Email: J.Taylor5@pgr.reading.ac.uk

Projecting the impacts of climate change on biodiversity is important for informing

Mauritius Kestrel by Joe Taylor
Male Mauritius kestrel (Falco punctatus) in the Bambous Mountains, eastern Mauritius. Photo by Joe Taylor.

mitigation and adaptation strategies. There are many studies that project climate change impacts on biodiversity; however, changes in the occurrence of extreme weather events are often omitted, usually because of insufficient understanding of their ecological impacts. Yet, changes in the frequency and intensity of extreme weather events may pose a greater threat to ecosystems than changes in average weather regimes (Jentsch and Beierkuhnlein 2008). Island species are expected to be particularly vulnerable to climate change pressures, owing to their inherently limited distribution, population size and genetic diversity, and because of existing impacts from human activities, including habitat destruction and the introduction of non-native species (e.g. Fordham and Brook 2010).

Mauritius is an icon both of species extinction and the successful recovery of threatened species. However, the achievements made through dedicated conservation work and the investment of substantial resources may be jeopardised by future climate change. Conservation programmes in Mauritius have involved the collection of extensive data on individual animals, creating detailed longitudinal datasets. These provide the opportunity to conduct in-depth analyses into the factors that drive population trends.

My study focuses on the demographic impacts of weather conditions, including extreme events, on three globally threatened bird species that are endemic to Mauritius. I extended previous research into weather impacts on the Mauritius kestrel (Falco punctatus), and applied similar methods to the echo parakeet (Psittacula eques) and Mauritius fody (Foudia rubra). The kestrel and parakeet were both nearly lost entirely in the 1970s and 1980s respectively, having suffered severe population bottlenecks, but all three species have benefitted from successful recovery programmes. I analysed breeding success using generalised linear mixed models and analysed survival probability using capture-mark-recapture models. Established weather indices were adapted for use in this study, including indices to quantify extreme rainfall, droughts and tropical cyclone activity. Trends in weather indices at key conservation sites were also analysed.

The results for the Mauritius kestrel add to a body of evidence showing that precipitation is an important limiting factor in its demography and population dynamics. The focal population in the Bambous Mountains of eastern Mauritius occupies an area in which rainfall is increasing. This trend could have implications for the population, as my analyses provide evidence that heavy rainfall during the brood phase of nests reduces breeding success, and that prolonged spells of rain in the cyclone season negatively impact the survival of juveniles. This probably occurs through reductions in hunting efficiency, time available for hunting and prey availability, so that kestrels are unable to capture enough prey to sustain themselves and feed their young (Nicoll et al. 2003, Senapathi et al. 2011). Exposure to heavy and prolonged rainfall could also be a direct cause of mortality through hypothermia, especially for chicks if nests are flooded (Senapathi et al. 2011). Future management of this species may need to incorporate strategies to mitigate the impacts of increasing rainfall.

References:

Fordham, D. A. and Brook, B. W. (2010) Why tropical island endemics are acutely susceptible to global change. Biodiversity and Conservation 19(2): 329‒342.

Jentsch, A. and Beierkuhnlein, C. (2008) Research frontiers in climate change: Effects of extreme meteorological events on ecosystems. Comptes Rendus Geoscience 340: 621‒628.

Nicoll, M. A. C., Jones, C. G. and Norris, K. (2003) Declining survival rates in a reintroduced population of the Mauritius kestrel: evidence for non-linear density dependence and environmental stochasticity. Journal of Animal Ecology 72: 917‒926.

Senapathi, D., Nicoll, M. A. C., Teplitsky, C., Jones, C. G. and Norris, K. (2011) Climate change and the risks associated with delayed breeding in a tropical wild bird population. Proceedings of the Royal Society B 278: 3184‒3190.

Climate model systematic biases in the Maritime Continent

Email: y.y.toh@pgr.reading.ac.uk

The Maritime Continent commonly refers to the groups of islands of Indonesia, Borneo, New Guinea and the surrounding seas in the literature. My study area covers the Maritime Continent domain from 20°S to 20°N and 80°E to 160°E as shown in Figure 1. This includes Indonesia, Malaysia, Brunei, Singapore, Philippines, Papua New Guinea, Solomon islands, northern Australia and parts of mainland Southeast Asia including Thailand, Laos, Cambodia, Vietnam and Myanmar.

subsetF1
Figure 1: JJA precipitation (mm/day) and 850 hPa wind (m s−1) for (a) GPCP and ERA-interim, (b) MMM biases and (c)–(j) AMIP biases for 1979–2008 over the Maritime Continent region (20°S–20ºN, 80°E–160ºE). Third panel shows the Maritime Continent domain and land-sea mask

The ability of climate model to simulate the mean climate and climate variability over the Maritime Continent remains a modelling challenge (Jourdain et al. 2013). Our study examines the fidelity of Coupled Model Intercomparison Project phase 5 (CMIP5) models at simulating mean climate over the Maritime Continent. We find that there is a considerable spread in the performance of the Atmospheric Model Intercomparison Project (AMIP) models in reproducing the seasonal mean climate and annual cycle over the Maritime Continent region. The multi-model mean (MMM) (Figure 1b) JJA precipitation and 850hPa wind biases with respect to observations (Figure 1a) are small compared to individual model biases (Figure 1c-j) over the Maritime Continent. Figure 1 shows only a subset of Fig. 2 from Toh et al. (2017), for the full figure and paper please click here.

We also investigate the model characteristics that may be potential sources of bias. We find that AMIP model performance is largely unrelated to model horizontal resolution. Instead, a model’s local Maritime Continent biases are somewhat related to its biases in the local Hadley circulation and global monsoon.

cluster2
Figure 2: Latitude-time plot of precipitation zonally averaged between 80°E and 160°E for (a) GPCP, (b) Cluster I and (c) Cluster II. White dashed line shows the position of the maximum precipitation each month. Precipitation biases with respect to GPCP for (d) Cluster I and (e) Cluster II.

To characterize model systematic biases in the AMIP runs and determine if these biases are related to common factors elsewhere in the tropics, we performed cluster analysis on Maritime Continent annual cycle precipitation. Our analysis resulted in two distinct clusters. Cluster I (Figure 2b,d) is able to reproduce the observed seasonal migration of Maritime Continent precipitation, but it overestimates the precipitation, especially during the JJA and SON seasons. Cluster II (Figure 2c,e) simulate weaker seasonal migration of Intertropical Convergence Zone (ITCZ) than observed, and the maximum rainfall position stays closer to the equator throughout the year. Tropics-wide properties of clusters also demonstrate a connection between errors at regional scale of the Maritime Continent and errors at large scale circulation and global monsoon.

On the other hand, comparison with coupled models showed that air-sea coupling yielded complex impacts on Maritime Continent precipitation biases. One of the outstanding problems in the coupled CMIP5 models is the sea surface temperature (SST) biases in tropical ocean basins. Our study highlighted central Pacific and western Indian Oceans as the key regions which exhibit the most surface temperature correlation with Maritime Continent mean state precipitation in the coupled CMIP5 models. Future work will investigate the impact of SST perturbations in these two regions on Maritime Continent precipitation using Atmospheric General Circulation Model (AGCM) sensitivity experiments.

 

 

References:

Jourdain N.C., Gupta A.S., Taschetto A.S., Ummenhofer C.C., Moise A.F., Ashok K. (2013) The Indo-Australian monsoon and its relationship to ENSO and IOD in reanalysis data and the CMIP3/CMIP5 simulations. Climate Dynamics. 41(11–12):3073–3102

Toh, Y.Y., Turner, A.G., Johnson, S.J., & Holloway, C.E. (2017). Maritime Continent seasonal climate biases in AMIP experiments of the CMIP5 multimodel ensemble. Climate Dynamics. doi: 10.1007/s00382-017-3641-x

Tropical Circulation viewed as a heat engine

Climate scientists have a lot of insight into the factors driving weather systems in the mid-latitudes, where the rotation of the earth is an important influence. The tropics are less well served, and this can be a problem for global climate models which don’t capture many of the phenomena observed in the tropics that well.

What we do know about the tropics however is that despite significant contrasts in sea surface temperatures (Fig. 1) there is very little horizontal temperature variation in the atmosphere (Fig. 2) – because the Coriolis force (due to the Earth’s rotation) that enables this gradient in more temperate climates is not present. We believe that the large-scale circulation acts to minimise the effect these surface contrasts have higher up. This suggests a model for vertical wind which cools the air over warmer surfaces and warms it where the surface is cool, called the Weak Temperature Gradient (WTG) Approximation, that is frequently used in studying the climate in the tropics.

GrSEMtest1_SST_map2-page-001
Fig.1 Sea surface temperatures (K) at 0Z on 1/1/2000 (ERA-Interim)
GrSEMtest1_T_map2-page-001
Fig.2 Temperatures at 500 hPa (K) at 0Z on 1/1/2000 (ERA-Interim)

 

 

 

 

 

Thermodynamic ideas have been around for some 200 years. Carnot, a Frenchman worried about Britain’s industrial might underpinning its military potential(!), studied the efficiency of heat engines and showed that the maximum mechanical work generated by an engine is determined by the ratio of the temperatures at which energy enters and leaves the system. It is possible to treat climate systems as heat engines – for example Kerry Emanuel has used Carnot’s idea to estimate the pressure in the eye of a hurricane. I have been building on a recent development of these ideas by Olivier Pauluis at New York University who shows how to divide up the maximum work output of a climate heat engine into the generation of wind, the lifting of moisture and a lost component, which he calls the Gibbs penalty, which is the energetic cost of keeping the atmosphere moist. Typically, 50% of the maximum work output is gobbled up by the Gibbs penalty, 30% is the moisture lifting term and only 20% is used to generate wind.

For my PhD, I have been applying Pauluis’ ideas to a modelled system consisting of two connected tropical regions (one over a cooler surface than the other), which are connected by a circulation given by the weak temperature gradient approximation. I look at how this circulation affects the components of work done by the system. Overall there is no impact – in other words the WTG does not distort the thermodynamics of the underlying system – which is reassuring for those who use it. What is perhaps more interesting however, is that even though the WTG circulation is very weak compared to the winds that we observe in the two columns, it does as much work as is done by the cooler column – in other words its thermodynamic importance is huge. This suggests that further avenues of study may help us better express what drives the climate in the tropics.

Synchronisation: how can this help weather forecasts in the future?

Current numerical modelling and data assimilation methods still face problems in strongly nonlinear cases, like in convective scales. A different, but interesting tool to help overcome these issues can be found in the synchronisation theory.

It all started in 1665, when Christiaan Huygens, a Dutch scientist, discovered that his two pendulum clocks were suddenly oscillating in opposite directions, but in a synchronised way. He tried to desynchronise them, by perturbing randomly one of the clocks, but surprisingly, after some time, both devices were synchronised again. He has attributed the phenomenon to the frame both clocks were sharing and after that, synchronisation field was opened to the world.

figure1

Figure 1: A drawing by Christiaan Huygens of his experiment in 1665.

Nowadays, researchers use these synchronisation concepts to reach a main goal: synchronise a model (any) with the true evolution of a system, using measurements. And even when only a reduced part of this system is observed, synchronisation between models and the true state can still be achieved. This is quite similar to what data assimilation looks for, as it aims to synchronise a model evolution with the truth by using observations, finding the best estimate of the state evolution and its uncertainty.

So why not investigate the benefits of recent synchronisation findings and combine these concepts with a data assimilation methodology?

At the start of this project, the first noticeable step that should be taken was to open up the synchronisation field to higher-dimension systems, as the experiments performed in the area were all focused on low-dimension, non-realistic systems. To this end, a first new idea was proposed:  an ensemble version of a synchronisation scheme, what we are calling EnSynch (Ensemble Synchronisation). Tests with a partly observed 1000-dimension chaotic model show a very efficient correspondence between the model and the true trajectories, both for estimation and prediction periods. Figures 2 and 3 show how our estimates and the truth are on top of each other, i.e. synchronised. Note that we do not have observations for all of the variables in our system. So, it is amazing to obtain the same successful results for the observed and also for the unobserved variables in this system!

figure2

Figure 2: Trajectories of 2 variables (top:observed and bottom: unobserved). Blue lines: truth. Green lines: estimates/predictions. (Predictions start after the red lines, i.e. no data assimilation is used.)

figure3

Figure 3: Zoom in the trajectory of a variable, showing how the model matches with the truth. Blue line: truth. Red line: our model. Yellow dots: observations.

The second and main idea is to test a combination of this successful EnSynch scheme with a data assimilation method called Particle Filter. As a proper data assimilation methodology, a particle filter provides us the best estimation of the state evolution and its uncertainty. Just to illustrate the importance of data assimilation in following the truth, figure 4 compares the case of only counting on an ensemble of models running freely in a chaotic nonlinear system, with the case of a data assimilation method applied to it.

figure4

Figure 4: Trajectories of ensemble members. Blue: with data assimilation. Red: without data assimilation. Truth is in black.

Efficient results are found with the combination between the new EnSynch and the particle filters. An example is shown in figure 5, where particles (ensemble members) of an unobserved variable nicely follow the truth during the assimilation period and also during the forecast stage (after t=100).

figure5

Figure 5: Trajectory for an unobserved variable in a 1000-dimension system. Observations occur at every 10 time steps until t=100. Predictions start after t=100.

These results are motivating and the next and big step is to implement this combined system in a bigger atmospheric model.  This methodology has been shown to be a promising solution for strongly nonlinear problems and potential benefits are expected for numerical weather prediction in the near future.

References:

Rey, D., M. Eldridge, M. Kostuk, H. Abarbanel, J. Schumann-Bischoff, and U. Parlitz, 2014a: Accurate state and parameter estimation in nonlinear systems with sparse observations. Physics Letters A, 378, 869-873, doi:10.1016/j.physleta.2014.01.027.

Zhu, M., P. J. van Leeuwen, and J. Amezcua, 2016: Implicit equal-weights particle filter. Quart. J. Roy. Meteorol. Soc., 142, 1904-1919, doi:10.1002/qj.2784.