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A new method for generating ensemble predictions based on an ensemble of data assimilations has been developed. Using an ensemble of four-dimensional ensemble-variational minimizations provides an approach which is close to the Met Office's operational data assimilation system and less computationally expensive than other alternatives. In developing this system, several inflation schemes have been compared. One form of additive inflation, based on analysis increments, was developed and found to be very effective at increasing the overall ensemble spread and correcting systematic biases in the model. However, the analysis increments are not flow-dependent since they are randomly drawn from a long archive. It was decided to scale back their amplitude to avoid them dominating the overall performance. Of the other inflation schemes considered, it was found that relaxation-to-prior-perturbations was the most effective at maintaining the ensemble spread. However, this scheme also produced perturbations which are too large-scale and too balanced. The relaxation-to-prior-spread scheme performed well in many respects, but required a relaxation factor greater than one to produce an acceptable spread. Therefore these two schemes were combined in order to mitigate the drawbacks of each. This combination proved successful and was used in final testing of the ensemble against the currently operational ensemble transform Kalman filter (ETKF). The ETKF has its perturbations centred around a high-resolution ‘deterministic’ analysis. This was seen to be an important benefit, and the new ensemble system also benefited from being recentred around the high-resolution analysis. This recentred system has slightly lower forecast skill than the ETKF over a variety of variables, due to the fact that the spread of this ensemble is less than the spread of the ETKF ensemble. The deficiency of the spread of the new ensemble system will be addressed in ongoing work.

The method of ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is implemented in fully non-linear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires association with the method of quasi-static variational assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of ensemble Kalman filter (EnKF) and particle filter (PF). On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are significantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need for QSVA.

Hybrid four-dimensional ensemble-variational (4DEnVar) data assimilation is a method which avoids using a linear and adjoint model by relying on an input ensemble to propagate analysis increments in time. Previous studies have shown that hybrid 4DEnVar performs worse than hybrid four-dimensional variational (4D-Var) assimilation. Given hybrid 4DEnVar's heavy reliance on the ensemble, this comparison may be affected by the quality of the input ensemble. Here we investigate how improvements to the ensemble system affect hybrid 4D-Var and how they affect the comparison with hybrid 4DEnVar. Using the Met Office's operational ensemble generation scheme (the ensemble transform Kalman filter, ETKF) it is found that hybrid 4D-Var gains little benefit from using an enlarged ensemble as input (176 as opposed to 23 members). By contrast, hybrid 4DEnVar benefits more from the increased ensemble size, and it benefits further when the weighting given to the ensemble covariance is increased. Both data assimilation methods benefit when the input ensemble is changed from using the ETKF to using an ensemble of 4DEnVars. Both schemes also show further benefit when a large ensemble (200 members) of 4DEnVars is used, and when a large weight is given to the covariance information from this ensemble. Thus, improving the ensemble covariance used in assimilation (ensemble generation method and ensemble size) and increasing its weight can have substantial benefits. Given that both hybrid 4D-Var and hybrid 4DEnVar benefit from improvements to the input ensemble, the relative performance is largely unaffected by the ensemble changes and hybrid 4D-Var performs better than hybrid 4DEnVar for all input ensembles.

We show how to replace an ensemble of variational data assimilation minimizations by minimizations for the ensemble mean and the perturbations from it. Tests using the Met Office system show that this Mean–Pert method can give practically identical results at much reduced cost. This makes it a good candidate component when designing a cost-effective system for hybrid ensemble-variational data assimilation for numerical weather prediction.

Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte-Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called Ensemble Variational Assimilation (EnsVAR), is studied in the two parts of the paper on the non-linear low-dimensional Lorenz-96 chaotic system, the assimilation being performed by the standard variational proce- dure. In Part I, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered as a statistical estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for Ensemble Kalman Filter and Particle Filter (although at a higher cost). Globally similar results are obtained with the Kuramoto-Sivashinsky equation.

In Part II, the method of Ensemble Variational Assimilation (EnsVAR) is implemented in fully nonlinear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires to be used in association with the method of Quasi-Static Variational Assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of Ensemble Kalman Filter and Particle Filter. On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are signif- icantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need to resort to QSVA.

Data assimilation obtains improved estimates of the state of a physical system by dynamically combining imperfect model results with sparse and noisy observations of reality. Not all observations u...

A simplex-centroid experimental design was used for the optimization of both reducing and oxidizing improvers, namely Aspergillus oryzae S2 α-amylase (Amy), ascorbic acid (Asc), and glucose oxidase (GOD). This optimization was performed to enhance the dough and breadmaking qualities of soft French wheat flour and a composite counterpart that contained 30% Ukrainian wheat flour. Statistically significant correlations were calculated between the W index and textural parameters (e.g., dough chewiness and bread cohesiveness). The findings revealed that while the best mixture for French flour comprised 21.8% of Amy, 41.2% of Asc, and 37% of GOD, for the composite counterpart, it comprised 2.3% of Amy, 66% of Asc, and 31.7% of GOD. These optimized mixtures rearranged soft French wheat flour and its composite counterpart to a good quality and an improved flour texture, respectively. Additionally, they increased the loaf specific volumes of the breads made from soft French wheat flour and its counterpart by 25.8 and 45.43%, respectively, significantly decreased the breads' susceptibility to microbial contamination, and reclassified the breads as "good" in terms of sensory attributes.

The impact of Aspergillus tubingensis glucose oxidase (GOD) in combination with α-amylase and ascorbic acid on dough properties, qualities and shelf life of bread was investigated. Regression models of alveograph and texture parameters of dough and bread were adjusted. Indeed, the mixture of GOD (44 %) and ascorbic acid (56 %) on flour containing basal improver showed its potential as a corrective action to get better functional and rheological properties of dough and bread texture. Furthermore, wheat flour containing basal additives and enriched with GOD (63.8 %), ascorbic acid (32 %) and α- amylase (4.2 %) led to high technological bread making parameters, to decrease the crumb firmness and chewiness and to improve elasticity, adhesion, cohesion and specific volume of bread. In addition to that, the optimized formulation addition significantly reduced water activity and therefore decreased bread susceptibility to microbial spoilage. These findings demonstrated that GOD could partially substitute not only ascorbic acid but also α-amylase. The generated models allowed to predict the behavior of wheat flour containing additives in the range of values tested and to define the additives formula that led to desired rheological and baking qualities of dough. This fact provides new perspectives to compensate flour quality deficiencies at the moment of selecting raw materials and technological parameters reducing the production costs and facilitating gluten free products development. Graphical abstractᅟ.

Data assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent DA systems: the 4D-Var and the ensemble methods. The hybrid method described in this paper consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection, and are replaced by estimates of the analysis error obtained through a low-rank Hessian inverse approximation. The updated error covariance in one window can be used as the background covariance for the next window thus better capturing the ‘error of the day’. The numerical results for a non-linear model demonstrate how the hybrid method leads to a good estimate of the true error covariance, and improves the 4D-Var analysis results.

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different observation locations is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper proposes a new approach to characterizes the usefulness of different observation in four dimensional variational (4D-Var) data assimilation. Metrics from information theory are used to quantify the contribution of observations to decreasing uncertainty with which the system state is known. We derive ensemble based, computationally feasible procedures to estimate the information content of various observations.