Oceans in Weather and Climate Course 2018

email: r.frew@pgr.reading.ac.uk

Between the 11th-16th March myself and four other PhDs and post docs attended the Ocean in Weather and Climate (OiWC) course at the Met Office, Exeter. This NERC advanced training course was aimed at PhDs, postdocs and beyond. It provided a great opportunity to spend a week meeting other Oceanography researchers at varying stages of their career, and to expand your understanding of the oceans role in climate beyond the scope of your own work.

The week kicked off with an ice breaker where we had do some ‘Scientific speed dating’, chatting to other participants about: Where are you from? What do you work on? What is your main hobby? What is the biggest question in your field of research? This set the tone for a very interactive week full of interesting discussions between all attendees and speakers alike. Course participants were accommodated at The Globe Inn situated in Topsham, a cute village-sized town full of pastel-coloured houses, cosy pubs, art galleries, and beautiful riverside walks to stretch your legs in the evenings.

The days consisted of four 1.5 hour sessions, split up by caffeine and biscuit breaks to recharge before the next session.

Topics covered in the lecture-style talks included…

  • Dynamical Theory
  • Modelling the Ocean
  • Observations
  • Ocean-atmosphere coupling
  • Air-sea fluxes
  • High Resolution Ocean modelling in coupled forecast systems
  • The Meridional Overturning Circulation
  • The Southern Ocean in climate and climatic change
  • Climate variability on diurnal, seasonal, annual, inter-annual, decadal timescales
  • Climate extremes
  • Climate sensitivity, heat uptake and sea level.
A recurring figure of the week…. taken from Helene Hewitt’s talk on high resolution ocean modelling showing ocean surface currents from HadGEM3-based global coupled models at different resolutions (eddy resolving, eddy permitting and eddy parameterised).


All the talks were very interesting and were followed by some stimulating discussion. Each session provided an overview of each topic and an indication of the current research questions in each area at the moment.

In the post lunch session, there were group practical sessions. These explored observational ARGO float data and model output. The practicals, written in iPython notebooks, were designed to let us play with some data, giving us a series of questions to trigger group discussions to deepen understanding of topics covered that morning.

The course also included some ‘softer’ evening talks, giving research career advice in a more informal manner. Most evenings were spent exploring the lovely riverside walks and restaurants/pubs of Topsham. The final evening was spent all together at the Cosy Club in Exeter, rounding off a very interesting and enjoyable week!

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.

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.

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).

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).


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.

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.

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.

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.




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

New Forecast Model Provides First Global Scale Seasonal River Flow Forecasts


Over the past ~decade, extended-range forecasts of river flow have begun to emerge around the globe, combining meteorological forecasts with hydrological models to provide seasonal hydro-meteorological outlooks. Seasonal forecasts of river flow could be useful in providing early indications of potential floods and droughts; information that could be of benefit for disaster risk reduction, resilience and humanitarian aid, alongside applications in agriculture and water resource management.

While seasonal river flow forecasting systems exist for some regions around the world, such as the U.S., Australia, Africa and Europe, the forecasts are not always accessible, and forecasts in other regions and at the global scale are few and far between.  In order to gain a global overview of the upcoming hydrological situation, other information tends to be used – for example historical probabilities based on past conditions, or seasonal forecasts of precipitation. However, precipitation forecasts may not be the best indicator of floodiness, as the link between precipitation and floodiness is non-linear. A recent paper by Coughlan-de-Perez et al (2017), “should seasonal rainfall forecasts be used for flood preparedness?”, states:

“Ultimately, the most informative forecasts of flood hazard at the seasonal scale are streamflow forecasts using hydrological models calibrated for individual river basins. While this is more computationally and resource intensive, better forecasts of seasonal flood risk could be of immense use to the disaster preparedness community.”

twitter_screenshotOver the past months, researchers in the Water@Reading* research group have been working with the European Centre for Medium-Range Weather Forecasts (ECMWF), to set up a new global scale hydro-meteorological seasonal forecasting system. Last week, on 10th November 2017, the new forecasting system was officially launched as an addition to the Global Flood Awareness System (GloFAS). GloFAS is co-developed by ECMWF and the European Commission’s Joint Research Centre (JRC), as part of the Copernicus Emergency Management Services, and provides flood forecasts for the entire globe up to 30 days in advance. Now, GloFAS also provides seasonal river flow outlooks for the global river network, out to 4 months ahead – meaning that for the first time, operational seasonal river flow forecasts exist at the global scale – providing globally consistent forecasts, and forecasts for countries and regions where no other forecasts are available.

The new seasonal outlook is produced by forcing the Lisflood hydrological river routing model with surface and sub-surface runoff from SEAS5, the latest version of ECMWF’s seasonal forecasting system, (also launched last week), which consists of 51 ensemble members at ~35km horizontal resolution. Lisflood simulates the groundwater and routing processes, producing a probabilistic forecast of river flow at 0.1o horizontal resolution (~10km, the resolution of Lisflood) out to four months, initialised using the latest ERA-5 model reanalysis.

The seasonal outlook is displayed as three new layers in the GloFAS web interface, which is publicly (and freely) available at www.globalfloods.eu. The first of these gives a global overview of the maximum probability of unusually high or low river flow (defined as flow exceeding the 80th or falling below the 20th percentile of the model climatology), during the 4-month forecast horizon, in each of the 306 major world river basins used in GloFAS-Seasonal.

The new GloFAS Seasonal Outlook Basin Overview and River Network Layers.

The second layer provides further sub-basin-scale detail, by displaying the global river network (all pixels with an upstream area >1500km2), again coloured according to the maximum probability of unusually high or low river flow during the 4-month forecast horizon. In the third layer, reporting points with global coverage are displayed, where more forecast information is available. At these points, an ensemble hydrograph is provided showing the 4-month forecast of river flow, with thresholds for comparison of the forecast to typical or extreme conditions based on the model climatology. Also displayed is a persistence diagram showing the weekly probability of exceedance for the current and previous three forecasts.

The new GloFAS Seasonal Outlook showing the river network and reporting points providing hydrographs and persistence diagrams.

Over the coming months, an evaluation of the system will be completed – for now, users are advised to evaluate the forecasts for their particular application. We welcome any feedback on the forecast visualisations and skill – feel free to contact me at the email address below!

To find out more, you can see the University’s press release here, further information on SEAS5 here, and the user information on the seasonal outlook GloFAS layers here.

*Water@Reading is “a vibrant cross-faculty centre of research excellence at the University of Reading, delivering world class knowledge in water science, policy and societal impacts for the UK and internationally.”

Full list of collaborators: 

Rebecca Emerton1,2, Ervin Zsoter1,2, Louise Arnal1,2, Prof. Hannah Cloke1, Dr. Liz Stephens1, Dr. Florian Pappenberger2, Prof. Christel Prudhomme2, Dr Peter Salamon3, Davide Muraro3, Gabriele Mantovani3

1 University of Reading
3 European Commission JRC

Contact: r.e.emerton@pgr.reading.ac.uk

Sea ice is complicated, but do sea ice models need to be?

email: r.frew@pgr.reading.ac.uk

Sea ice is complex…

When sea water freezes it forms sea ice, a composite of ice and brine. Sea ice exhibits varying structural, thermodynamic and mechanical properties across a range of length- and time-scales. It can be subcategorised into numerous different types of sea ice depending on where is grows and how old it is.



Different sea ice growth processes and types 1.

However, climate models do not simulate the evolution of floes (they model floes as cylindrical) or the floe size distribution, which has implications for ice melt rates and exchange of heat with the atmosphere and ocean. Sea ice also hosts algae and small organisms within brine channels in the ice, which can be important for nutrient cycles. This is a developing area of earth system modelling.

Schematic of life within brine channels in sea ice 2.

How much complexity do global climate models need to sufficiently model the interactions of sea ice with the ocean and atmosphere?
The representation of sea ice in global climate models is actually very simple, with minimal sea ice types and thickness categories. The main important feature of sea ice for global climate models is its albedo, which is much greater than that of open water, making it important for the surface energy balance. So, it is important to get the correct area of sea ice. Global climate models need sea ice:

  • to get the correct heat exchange with the atmosphere and ocean
  • to get a realistic overturning circulation in the ocean.
  • because salt release during sea ice growth is important for the ocean salinity structure, and therefore important to get the correct amount of sea in/near deep water formation sites.
  • sea ice is not important for sea level projections.

So, do the complex features of sea ice matter, or are simple parameterisations sufficient?

Sea_ice_Drawing_General_features.svg Schematic showing some dynamic features of sea ice 3.

Which leads to a lot more questions…

  • Where does the balance between sufficient complexity and computational cost lie?
  • Does adding extra model complexity actually make it harder to understand what the model is doing and therefore to interpret the results?
  • Do climate models need any further improvements to sea ice in order to better simulate global climate? There is still large uncertainty surrounding other climate model components, such as clouds and ocean eddies, which are believed to explain a lot of the discrepancy between models and observations, particularly in the Southern Ocean.

A lot of these questions depend on the scientific question that is being asked. And the question is not necessarily always ‘how is global climate going to change in the future’. Sea ice is fascinating because of its complexity, and there are still many interesting questions to investigate, hopefully before it all melts!

 Images clockwise from top left: grease ice 4, pancake ice 5, surface melt ponds 6, ice floes 7

The Future Developments in Climate Sea Ice Modelling Workshop

This blog stems from a one day workshop I attended on ‘Future developments in climate sea ice modelling’ at the Isaac Newton Centre as part of a four month programme on the ‘Mathematics of Sea Ice Phenomena’. The format of the day was that three different strands of sea ice researchers gave 40 min talks giving their strand’s point of view of current sea ice developments and what the focus should be for sea ice modelers, each followed by 40 mins of open discussion with the audience.

The three (very good!) talks were:

  1. Dirk Notz: What do climate models need sea ice for? A top-down, system level view of what sea ice models should produce from the perspective of a climate modeller.
  2. Cecilia Bitz: What sea ice physics is missing from models? A bottom-up view of what is missing from current sea ice models from the perspective of a sea ice scientist.
  3. Elizabeth Hunke: What modelling approaches can be used to address the complexity of sea ice and the needs of climate models?


  1. https://nsidc.org/cryosphere/seaice/characteristics/formation.html.
  2. https://www.eduplace.com/science/hmxs/ls/mode/cricket/sect7cc.shtml
  3. https://en.wikipedia.org/wiki/Fast_ice
  4. https://www.travelblog.org/Photos/2101807
  5. http://www.antarctica.gov.au/about-antarctica/environment/icebergs-and-ice/sea-ice
  6. https://en.wikipedia.org/wiki/Sea_ice#/
  7. https://www.shutterstock.com/video/clip-15391768-stock-footage-flying-over-arctic-ice-floes.html

Adventures in Modelling – NCAS Climate Modelling Summer School

At the beginning of September 3 PhD students from Reading, including myself, went to Cambridge to attend the NCAS Climate Modelling Summer School. This is an annual event aimed at PhD students and early career scientists who want to develop their understanding of climate models, with topics covering parameterisations to supercomputers.

Staff and students of the course pose outside the Chemistry department, which played host to morning lectures

The course ran over two weeks with lectures on the components of climate models in the morning, covering fundamental dynamics and thermodynamics, numerical methods and different parameterisations. This was followed by an afternoon of computer practicals and then more topical lectures in the evening, such as “User engagement in climate science” and “The Sun and Earth’s climate system”. The lectures were very fast paced but this was a great opportunity to cover so many topics in a short space of time and get a grounding in lots of different topics that I will definitely be looking over in future. A poster session on the second evening gave us the chance to learn about other people’s work and make connections with other people starting out their careers in climate science, including a few readers of the blog, that will hopefully last throughout our careers.

One of the highlights of the course was the chance to run some (rather interesting) experiments with an earth system model. This involved breaking into groups with each being given a different project. It was exciting to go  through the whole process of having an idea, developing a hypothesis, thinking of specific experiments to answer the hypothesis and then analysing the results in just a week – something that takes much longer when you’re doing a PhD! My group worked on the Flat Earth experiment, which looked at the effect of removing all of the earth’s orography not, to our dismay, turning the earth into a flat disk. I learned a lot about how to run models, something which I have never done even though I use the output. It also developed my understanding of different climate processes that I don’t work with such as the monsoons, and even dynamical vegetation.

Flat earth experiment looking at the change in the monsoon winds

Throughout the course we stayed at St Catharine’s College. Right in the centre of Cambridge it quickly felt like a home from home, keeping us well fed to get through the intense science. Although the weekend was rainy, apparently breaking a run of excellent weather for the school, we still had plenty of time to explore beautiful Cambridge. A few people were even brave enough to go punting!

An interesting, hectic and inspiring two weeks later we may have been glad to head back to Reading for a good sleep but having thoroughly enjoyed the summer school.

The beautiful St Catharine’s College, image from http://www.caths.cam.ac.uk/


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.


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!


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.)


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.


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).


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.


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.