Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

How essential are Argo observations to constrain a global ocean data assimilation system?

Observing system experiments (OSEs) are carried out over a 1-year period to quantify the impact of Argo observations on the Mercator Ocean 0.25° global ocean analysis and forecasting system. The reference simulation assimilates sea surface temperature (SST), SSALTO/DUACS (Segment Sol multi-missions dALTimetrie, d'orbitographie et de localisation précise/Data unification and Altimeter combination system) altimeter data and Argo and other in situ observations from the Coriolis data center. Two other simulations are carried out where all Argo and half of the Argo data are withheld. Assimilating Argo observations has a significant impact on analyzed and forecast temperature and salinity fields at different depths. Without Argo data assimilation, large errors occur in analyzed fields as estimated from the differences when compared with in situ observations. For example, in the 0–300 m layer RMS (root mean square) differences between analyzed fields and observations reach 0.25 psu and 1.25 °C in the western boundary currents and 0.1 psu and 0.75 °C in the open ocean. The impact of the Argo data in reducing observation–model forecast differences is also significant from the surface down to a depth of 2000 m. Differences between in situ observations and forecast fields are thus reduced by 20 % in the upper layers and by up to 40 % at a depth of 2000 m when Argo data are assimilated. At depth, the most impacted regions in the global ocean are the Mediterranean outflow, the Gulf Stream region and the Labrador Sea. A significant degradation can be observed when only half of the data are assimilated. Therefore, Argo observations matter to constrain the model solution, even for an eddy-permitting model configuration. The impact of the Argo floats' data assimilation on other model variables is briefly assessed: the improvement of the fit to Argo profiles do not lead globally to unphysical corrections on the sea surface temperature and sea surface height. The main conclusion is that the performance of the Mercator Ocean 0.25° global data assimilation system is heavily dependent on the availability of Argo data.

Data assimilation for advanced cross-scale unstructured-grid ocean modeling.

The coastal ocean is a complex environment with extremely dynamic processes that require a high-resolution and cross-scale modeling approach in which all hydrodynamic fields and scales are considered integral parts of the overall system. In the last decade, unstructured-grid models have been used to advance in seamless modeling between scales. On the other hand, the data assimilation methodologies to improve the unstructured-grid models in the coastal seas have been developed only recently and need significant advancements. Here, we link the unstructured-grid ocean modeling to the variational data assimilation methods. In particular, we show results from the modeling system SANIFS based on SHYFEM fully-baroclinic unstructured-grid model interfaced with OceanVar, a state-of-art variational data assimilation scheme adopted for several systems based on a structured grid. OceanVar implements a 3DVar DA scheme. The combination of three linear operators models the background error covariance matrix. The vertical part is represented using multivariate EOFs for temperature, salinity, and sea level anomaly. The horizontal part is assumed to be Gaussian isotropic and is modeled using a first-order recursive filter algorithm designed for structured and regular grids. Here we introduced a novel recursive filter algorithm for unstructured grids. A local hydrostatic adjustment scheme models the rapidly evolving part of the background error covariance. We designed two data assimilation experiments using SANIFS implementation interfaced with OceanVar over the period 2017-2018, one with only temperature and salinity assimilation by Argo profiles and the second also including sea level anomaly. The results showed a successful implementation of the approach and the added value of the assimilation for the active tracer fields. While looking at the broad basin, no significant improvements are highlighted for the sea level, requiring future investigations. Furthermore, a Machine Learning methodology based on an LSTM network has been used to predict the model SST increments.

Data assimilation: From photon counts to Earth System forecasts

Data assimilation – the set of techniques whereby information from observing systems and models is combined optimally – is rapidly becoming prominent in endeavours to exploit Earth Observation for Earth sciences, including climate prediction. This paper explains the broad principles of data assimilation, outlining different approaches (optimal interpolation, three-dimensional and four-dimensional variational methods, the Kalman Filter), together with the approximations that are often necessary to make them practicable. After pointing out a variety of benefits of data assimilation, the paper then outlines some practical applications of the exploitation of Earth Observation by data assimilation in the areas of operational oceanography, chemical weather forecasting and carbon cycle modelling. Finally, some challenges for the future are noted.