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.


Tales from the Alice Holt forest: carbon fluxes, data assimilation and fieldwork


Forests play an important role in the global carbon cycle, removing large amounts of CO2 from the atmosphere and thus helping to mitigate the effect of human-induced climate change. The state of the global carbon cycle in the IPCC AR5 suggests that the land surface is the most uncertain component of the global carbon cycle. The response of ecosystem carbon uptake to land use change and disturbance (e.g. fire, felling, insect outbreak) is a large component of this uncertainty. Additionally, there is much disagreement on whether forests and terrestrial ecosystems will continue to remove the same proportion of CO2 from the atmosphere under future climate regimes. It is therefore important to improve our understanding of ecosystem carbon cycle processes in the context of a changing climate.

Here we focus on the effect on ecosystem carbon dynamics of disturbance from selective felling (thinning) at the Alice Holt research forest in Hampshire, UK. Thinning is a management practice used to improve ecosystem services or the quality of a final tree crop and is globally widespread. At Alice Holt a program of thinning was carried out in 2014 where one side of the forest was thinned and the other side left unmanaged. During thinning approximately 46% of trees were removed from the area of interest.

Figure 1: At the top of Alice Holt flux tower.

Using the technique of eddy-covariance at flux tower sites we can produce direct measurements of the carbon fluxes in a forest ecosystem. The flux tower at Alice Holt has been producing measurements since 1999 (Wilkinson et al., 2012), a view from the flux tower is shown in Figure 1. These measurements represent the Net Ecosystem Exchange of CO2 (NEE). The NEE is composed of both photosynthesis and respiration fluxes. The total amount of carbon removed from the atmosphere through photosynthesis is termed the Gross Primary Productivity (GPP). The Total Ecosystem Respiration (TER) is made up of autotrophic respiration (Ra) from plants and heterotrophic respiration (Rh) from soil microbes and other organisms incapable of photosynthesis. We then have, NEE = -GPP + TER, so that a negative NEE value represents removal of carbon from the atmosphere and a positive NEE value represents an input of carbon to the atmosphere. A schematic of these fluxes is shown in Figure 2.

Figure 2: Fluxes of carbon around a forest ecosystem.

The flux tower at Alice Holt is on the boundary between the thinned and unthinned forest. This allows us to partition the NEE observations between the two areas of forest using a flux footprint model (Wilkinson et al., 2016). We also conducted an extensive fieldwork campaign in 2015 to estimate the difference in structure between the thinned and unthinned forest. However, these observations are not enough alone to understand the effect of disturbance. We therefore also use mathematical models describing the carbon balance of our ecosystem, here we use the DALEC2 model of ecosystem carbon balance (Bloom and Williams, 2015). In order to find the best estimate for our system we use the mathematical technique of data assimilation in order to combine all our available observations with our prior model predictions. More infomation on the novel data assimilation techniques developed can be found in Pinnington et al., 2016. These techniques allow us to find two distinct parameter sets for the DALEC2 model corresponding to the thinned and unthinned forest. We can then inspect the model output for both areas of forest and attempt to further understand the effect of selective felling on ecosystem carbon dynamics.

Figure 3: Model predicted cumulative fluxes for 2015 after data assimilatiom. Solid line: NEE, dotted line: TER, dashed line: GPP. Orange: model prediction for thinned forest, blue: model prediction for unthinned forest. Shaded region: model uncertainty after assimilation (± 1 standard deviation).

In Figure 3 we show the cumulative fluxes for both the thinned and unthinned forest after disturbance in 2015. We would probably assume that removing 46% of the trees from the thinned section would reduce the amount of carbon uptake in comparison to the unthinned section. However, we can see that both forests removed a total of approximately 425 g C m-2 in 2015, despite the thinned forest having 46% of its trees removed in the previous year. From our best modelled predictions this unchanged carbon uptake is possible due to significant reductions in TER. So, even though the thinned forest has lower GPP, its net carbon uptake is similar to the unthinned forest. Our model suggests that GPP is a main driver for TER, therefore removing a large amount of trees has significantly reduced ecosystem respiration. This result is supported by other ecological studies (Heinemeyer et al., 2012, Högberg et al., 2001, Janssens et al., 2001). This has implications for future predictions of land surface carbon uptake and whether forests will continue to sequester atmospheric CO2 at similar rates, or if they will be limited by increased GPP leading to increased respiration.


Wilkinson, M. et al., 2012: Inter-annual variation of carbon uptake by a plantation oak woodland in south-eastern England. Biogeosciences, 9 (12), 5373–5389.

Wilkinson, M., et al., 2016: Effects of management thinning on CO2 exchange by a plantation oak woodland in south-eastern England. Biogeosciences, 13 (8), 2367–2378, doi: 10.5194/bg-13-2367-2016.

Bloom, A. A. and M. Williams, 2015: Constraining ecosystem carbon dynamics in a data-limited world: integrating ecological “common sense” in a model data fusion framework. Biogeosciences, 12 (5), 1299–1315, doi: 10.5194/bg-12-1299-2015.

Pinnington, E. M., et al., 2016: Investigating the role of prior and observation error correlations in improving a model forecast of forest carbon balance using four-dimensional variational data assimilation. Agricultural and Forest Meteorology, 228229, 299 – 314, doi:

Heinemeyer, A., et al., 2012: Exploring the “overflow tap” theory: linking forest soil co2 fluxes and individual mycorrhizo- sphere components to photosynthesis. Biogeosciences, 9 (1), 79–95.

Högberg, P., et al., 2001: Large-scale forest girdling shows that current photosynthesis drives soil respiration. Nature, 411 (6839), 789–792.

Janssens, I. A., et al., 2001: Productivity overshadows temperature in determining soil and ecosystem respiration across european forests. Global Change Biology, 7 (3), 269–278, doi: 10.1046/j.1365-2486.2001.00412.x.

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